There are actually two questions here, one broader than the other
Why would Russia care about NATO troops on its borders if it has nuclear weapons?
But why would Russia fear a land-based invasion from NATO in the first place?
Russia, to my recollection, has seldom complained about the latter but a lot about the former. It's alas a lot of Western armchair strategists (journalists, youtubers, posters here) who assert by pointing to WW2 etc. that Russia fears NATO ground invasion.
To give you some concrete examples of the more common/mundane complaints that Russia did raise in the years past:
- when Western NATO aircraft first deployed to Latvia, Russia complained that NATO AWACS could then see "deep" in its territory.
When NATO sent an AWACS reconnaissance aircraft to Rumbula Airfield in Latvia on Feb. 23  and then to Siauliai two days later on what NATO called a demonstration flight, Russian officials angrily protested that the plane's sophisticated radar equipment could peer deep into European Russia.
- when the US deployed that "AEGIS ashore" missile base in Romania (and Poland),
The United States switched on an $800 million missile shield in Romania yesterday (12 May ) that it sees as vital to defend itself and Europe from so-called rogue states but the Kremlin says is aimed at blunting its own nuclear arsenal.
In fact Putin himself addressed that one with many more words when the base was under construction (2016):
Speaking to Russian officials in Moscow, Mr Putin said: "This is not a defence system. This is part of a US nuclear strategic potential brought on to a periphery.
"In this case, Eastern Europe is such a periphery. Those people taking such decisions must know that until now they have lived calm, fairly well-off and in safety.
"Now, as these elements of ballistic missile defence are deployed, we are forced to think how to neutralise the emerging threats to the Russian Federation."
Now, I don't exclude that with the heightened rhetoric from last year, and their demand that Western NATO forces retreat to pre-1997 positions, Russia may have asserted NATO had broader aims, but I don't recall a ground invasion being mentioned specifically by official Russian sources. They do generally say that NATO bases are surrounding Russia and the like, but their specific complaints seldom (if ever) mention a ground invasion, from my recollection. I'm not too surprised since Eastern European members of NATO have armies that are qualitatively and quantitively below that of Russia, and the number of Western NATO forces in that regions was relatively limited compared to either Russian deployments on their side of the border or even with what the US e.g. mustered on some middle-eastern bases not so long ago, never mind in Western Europe. To wit, there are some 100,000 US troops in Europe but only about 16,000 Western NATO/US troops in Eastern European NATO members.
I managed to find a balance of ground forces assessment in the Baltics from 2020:
Russia keeps around 760 tanks in 25 battalions within quick striking distance of NATO's Baltic members. NATO countries together maintain 15 battalions with around 130 tanks in the same region — and around 90 of those are the American M-1s on their temporary rotation.
I (finally) managed to find a statement of Putin from December 2021, in which he explains that Russia fears the deployment of US hypersonic weapons in Ukraine, and that under their cover "extremists" will attack Crimea:
The United States and its allies need to understand that Russia simply "has nowhere to retreat" if its weapons appear in Ukraine, Russian President Vladimir Putin said on Tuesday at an expanded meeting of the Defense Ministry board.
"They [the US] simply do what they want. But what they are doing on the territory of Ukraine now, or trying to do and going to do — this is not thousands of kilometers away from our national border. This is at the doorstep of our home. They must understand that we simply have nowhere to retreat further," Putin said.
"We have specialists here, we are in constant contact with them. There is no hypersonic weapon in the United States yet, but we know when it will appear — they cannot hide it, everything is recorded, the tests are being conducted, successfully or unsuccessfully. So we approximately understand when it will happen," the President added.
Putin also believes that if the US deploys its weapons in Ukraine, it may try under the cover of these weapons to push Kiev to attack Crimea.
"They will put hypersonic weapons in Ukraine, and then, under their cover <...> they will arm and push extremists from the neighboring state against Russia, including into certain regions of the Russian Federation, for example, Crimea, under advantageous circumstances as they believe," the head of state went on.
The scenario seems somewhat fantastical, but I guess he's afraid that hypersonic weapons in Ukraine might negate the large numerical advantage that the Russian navy has on the Black Sea.