(note: I voted to close this Q. Since it got reopened and has no pending close votes, I'll instead try to explain why, IMHO, it can't be answered as asked).
We don't know what they'll resort to next. When it happens, we'll see. Or not - (see ongoing debate re. Bakhmut
** strategic efficiency).
Asking this question is understandable. Expecting it to be answered definitively is however unrealistic.
What has Russia stated?
Russia has stated very little to date. Putin has not even clearly articulated his overall political war aims besides de-Nazification, blocking NATO and annexing 4 Ukrainian regions.
Why would we expect him to communicate their military strategies??? Doing so would a) allow Ukraine to develop plans to counteract them and b) commit Putin and MoD to certain goals which would look bad domestically if they weren't met.
Military strategies are usually kept secret in wars.
Maybe too many of us have been brought up in the 2004+ timeline of communicated strategies by the US DoD about Iraq and Afghanistan: "we plan a surge", "we plan to develop the countryside", "we plan to transition to national forces". A counter insurgency war demands clear communication of to the local population and to the population back at home which has no direct risk from a war they are funding and a has say. That's why you have these statements of intent.
Ukraine 2022 is not that war. It's more akin to WW2, where strategic misdirection was a common ploy (or Ukraine's announcement of "all in for Kherson" in July/August).
What's are they gonna do, from their options?
Wear down the Ukrainian/NATO forces in terms of personnel, equipment or ordnance, until they can no longer maintain their stance?
Win the war piecemeal, by taking one town after another? (And if so - how does this square with the organized retreat from Kherson?
Go out on a significant offensive at some point in the near future?
Keep a "draw" with hopefully small losses, until NATO, the US or the EU agree to negotiate a political arrangement?
Any of them are candidates. Either one after another or simultaneously. All of these seem valid approaches. Maybe they'll try one, then shift to another? Maybe they'll do any of these in the short term, but hope to cash in on Western weariness and energy insecurity in winter 2023? More people can chip in with more options to choose from.
After a year of operation...
We can see Russia has followed several strategies:
Decapitation of existing Ukraine regime, until April
Grinding battle of attrition and territorial acquisition - Severodonestk - until Sept
Defense, then force conservation - Kherson
* - until Dec
Back to grinding - ongoing
** being one location, but they are attacking at many locations.
We also see a strategy of attacking civilian energy infrastructure.
They haven't stated their reasons there, but the Western press consensus is to use their vergeltungswaffen to terrorize the population, which is brutish but unlikely to work. On the other hand, people like Kofman (War on the Rocks) state that there is a major economic risk by a) shooting down cheap plentiful missiles with costly, scarce, counter missiles and b) driving down Ukraine GDP which will require even more Western cash infusion to keep Ukraine, the country going, on top of weapon donations.
Which is it? Gotta read Putin's and his pals mind for that.
Limits of analysis
We have had a number of major strategic possible axis of action by Putin and the gang.
- use, or not of nukes
- re-invasion from Belarus
- round 2 of mobilization
- state of Putin's constraints wrt Russian public opinion support/opposition to war
Besides a lot of poor trees being cut down to chat about these, what have we learned, concretely, about their intentions? Very little. Even the pronouncements by different actors - Medvedev re. nukes, round #2 of mobilization by Ukraine intelligence have political motivations for being made.
A lot of what we are told in the Western media is gleaned by analyzing milbloggers, or by listening to Ukraine PR, which has its own agenda.
Another risk in assessing possible strategies is that most Western press tends to summarily dismiss most Russian military activities as being brutish and inefficient. Yes, it has been mostly so, to date, but the risk remains that they may yet learn (Russia's military leadership in '44/45 was light years past its '41 version).
Russia's "strategy" seems driven very much from the top
So there is little to be known about it beforehand without reading Putin's mind.
For example, the numerous reports of soldiers thinking they were still on maneuvers and exercises Feb 23 and 24, 2022, right as they were invading. As well as the near-constant rotation of top commanders. So it is secretive, capricious and not always best practices in military terms (way too much diffusion of efforts in the first phase and under-use of aviation).
I could make a comparison to Hitler dictating illogical military strategies in late WW2, but I know that will upset Russians, so I'll use one which should make them much happier: Stalin dictating illogical military strategies in early WW2 (before he let the generals do their job).
Without deep access to Russian leadership's thinking we can't say for sure. Only hypothesize. And even then that is limited by trying to apply logic to a war which seems, at core, illogical. Both in starting it ("The only winning move is not to play"), or the way Russia has failed at effectively prosecuting it.
p.s. what we do know
Russia has mobilized 300+k men. Only some of them had been used until mid-January, to stiffen resistance in the Kreminna area. They have the rest to do something with or train some more.
Mud season starts in mid/late March and will last into summer
Russia may want to do something before the 150-ish Western modern main battle tanks make it to the front, which will be 4-6 weeks at least.
Russia used to "spend" lots of armor to conserve manpower. Now, it has reversed, especially in Bakhmut. They husband their hardware, but throw lots of warm bodies. Does that mean they've given up on maneuver warfare? Are they saving their gear for a big offensive?
Putin has given no serious indication of negotiation. Russia is somewhat restructuring its economy to strengthen their military industrial complex, which indicates wanting to stick it out.
Russian wunderwaffen aren't very wonderful or plentiful and are being kept out of harms way in Ukraine (Armata tanks, Su-57). T-62s seem considerably more on the menu, perhaps indicative of having to fight with men rather than equipment in the future (which might lead to more slow attrition like we are seeing now, maybe at higher scale. Rather than any novel strategies).
Russia is getting more disciplined. They are digging defensive positions and being more careful, have lots more troops and have a much shorter front. On the defense, they won't be as easy to catch with their pants down a la Kharkiv/Izyum.
Russia has annexed several regions in their entirety and Crimea too. Until such time as Putin walks that back, they will want to capture all of their territory, because they are "Mother Russia Land". Due to the river, Kherson is somewhat out of the question and they already have Crimea. That leaves the others.
It is hard to see how Russian atrocities in Bucha and other areas would be conducive to achieving limited goals by Russia without needing to first fully defeat by Ukraine by force of arms or by starvation from Western arms (donations which are rendered more politically palatable to Western publics due to Russian war crimes).
Comparisons to the casualties accepted by Russians in WW2 are misleading. Stalin had absolute power, backed by Gulags and the NKVD. But more importantly, Russians had no choice but to keep on fighting, having been designated, and treated, as "untermenschen" by the Nazis. Russia, in 2023, can... leave Ukraine. If anything the comparison applies more to Ukrainians who know to expect very little good from Russian governance.
This place had a strong potential to become a Russian Dien Bien Phu, with their best troops getting cut off from supplies across the river. Getting out was a military decision and, unfortunately, shows that at times Putin can be rational about respecting military necessities over political expediency.
In the case of an ongoing operation, Bakhmut, there is even disagreement in the Western press of what the strategy is there, with the overwhelming (but unconvincing) narrative being that is no military strategy at play, only political posturing within Russian elites, leading to massive losses.
Russia hasn't told us.
An alternative, less popular, more alarming, interpretation, Michael Kofman's for example, says that Ukraine is forced to trade good soldiers against throwaway low quality troops (convicts) and units outside the MoD (Wagner). And that, as we don't know the extent of UA losses we are unable to ascertain exactly how Bakhmut is playing out.
When judging whether UA is wise to hold out Bakhmut you may also want to assess if it's favorable enough terrain on the defense. If other areas in the vicinity are not as favorable, might as well hold out there.
Last, one thing we certainly know about Bakhmut is that Russia media is trumpeting their great achievements in almost conquering a city of 70000 after 5? months of going for it. If it falls, expect a Russian narrative of strategic genius and overwhelming victory. Like Sievierodonetsk which achieved little of the sort in hindsight.