Most clear "grand strategy" statement I've seen to date:
As we've been reporting, Israel's Prime Minister Benjamin Netanyahu earlier today [Oct 28] said his country's war with Hamas had entered its "second stage".
Last week, Israel's defence minister Yoav Gallant told a parliamentary committee that the war would have three stages.
"The first stage of the campaign was meant to destroy Hamas's infrastructure in order to defeat and destroy Hamas," Gallant said.
He described the second stage as continued fighting as troops work to “eliminate pockets of resistance".
And the third phase, Gallant said, "will require the removal of Israel's responsibility for life in the Gaza Strip, and the establishment of a new security reality for the citizens of Israel".
Since one may be curious what was achieved in the first phase, there's an attempted summary at end of this answer (3rd part).
Not a lot was shared about the vision for this 2nd phase, but
Defense Minister Yoav Gallant said Israel expects a long and difficult ground offensive into Gaza soon. It “will take a long time” to dismantle Hamas’ vast network of tunnels, he said, adding that he expects a lengthy phase of lower-intensity fighting as Israel destroys “pockets of resistance.”
Netanyahu himself has said pretty much the same:
The war will be "long and hard," warned Israeli Prime Minister Benjamin Netanyahu as he announced the launch of Israel's second phase in its war against Hamas militants in the Gaza Strip.
"This is the second stage of the war whose goals are clear — to destroy Hamas' governing and military capabilities and to bring the hostages home," Netanyahu told reporters Saturday night in Tel Aviv. He vowed that every effort would be made to rescue the more than 200 hostages held by Hamas.
"We are only at the start," he said. "We will destroy the enemy above ground and below ground."
Aside from that, in connection to US advisors being sent to Israel, the media and analysts cited the US experience with Mosul campaign (against ISIS), which took some nine months to complete, although it was initially planned to last just three. CNN actually has slightly more detail on that:
US military advisers on the ground in Israel are invoking lessons learned specifically from Fallujah in 2004, one of the bloodiest battles of the Iraq War.
Instead of launching a full-scale ground assault on Gaza, which could endanger hostages, civilians, and further inflame tensions in the region, US military advisers are urging Israelis to use a combination of precision airstrikes and targeted special operations raids.
They are also drawing on strategies developed during the battle by US-led coalition forces to retake the Iraqi city of Mosul from ISIS, which relied more heavily on special operations forces. Like Hamas, ISIS built tunnels throughout Mosul and used civilians as human shields, and the fight to retake the city was harder and more drawn-out than anticipated.
To help deliver this message, the Biden administration has sent a three-star Marine Corps general to counsel the IDF on planning its tactical assault. Gen. James Glynn, the former commander of Marine Forces Special Operations Command, has significant experience with urban warfare in Iraq, particularly in Fallujah, where he commanded troops during some of the bloodiest fighting there between US forces and insurgents, officials said. [...]
A senior Israeli official said that the US is not telling the Israelis to deescalate or refrain from crossing any “red lines.”
“They are saying while you fight the war – pay attention to all of these dimensions,” the official said. “The US has its own experience for fighting wars in urban areas, Fallujah, in Mosul and so on. … And so you [the United States] also have some experience in such a situation. And it’s always good to share experiences, among friends.”
What the IDF does have is a series of carefully worked out plans to destroy Hamas’ capabilities, according to a 2017 study by the Rand Corporation, a Washington think-tank with ties to the US military.
Ranked as small, medium and large, the plans were worked out before the IDF’s last ground invasion of Gaza in 2014.
The smallest one involved the IDF taking control of northern Gaza without entering populated areas — a situation similar to the current state of fighting there. The medium plan envisaged a larger ground incursion into northern and southern areas. The largest plan involved taking all of Gaza.
Although the plans remain secret, Israeli defence planners have worked out the forces needed to conduct each operation, according to the Rand study.
So, if I'm to abuse a phrase, this one is going according to the plan, for now.
Older answer below:
This answer may well be overtaken by events, but insofar there's no definitive answer, as far as I can tell.
According to commentators, Netanayahu previously has been reluctant to engage in ground incursions, preferring air strikes. He might not be able to stick just with that this time given the magnitude of the Hamas attacks.
In a previous case when Israeli troops did go into Gaza, i.e. 2014, their goals were mainly to find and destroy the tunnel network [parts] that could not be found & hit from the air. (Netanyahu was also PM back then, so clearly he's not completely against ground incursions.)
However, this time, some Israeli army spokesperson has hinted at potentially broader goals, saying that Hamas cannot be allowed to stay in power or even 'live'. (N.B., also quoted by VOA as saying "we are also to make sure that Hamas will not be able to govern the Gaza Strip".) They've [insofar] not said however how Israel is going to achieve these desiderata, i.e. just by air or what extent of ground attacks they envisage etc. Netanyahu himself has used strong terms like "defeat to death" of Hamas (sounds a little awkward in English, maybe someone has a better translation).
More recent reports say Israel has called "up to" 300,000 reservists and amassed troops on the border with Gaza, suggesting a large scale ground operation is going to take place, eventually. (FWTW, back in 2014, Israel called up much fewer reservists--they announced at most 40,000 back then.) Also, the US has called the recent attacks by Hamas, "ISIS-level savagery", suggesting they'd greenlight a similar level of measures that they had taken against ISIS, i.e. [near] total destruction of the group and its leadership, and depriving them [or any remnants] of the ability to control any significant territory, like the combined air-ground campaign against ISIS ended.
Also, a bit more recently, Netanyahu said Hamas is "worse than Daesh [ISIS]" and that "Every Hamas member is a dead man." So that seems to be the ideal goal for his government right now. Whether that's realistic remains to be seen. But he seems to have fairly broad political support for that, e.g.:
Mr Gantz told Israeli citizens that the newly-formed government was "united" and ready to "wipe this thing called Hamas off the face of the Earth".
As for more recent developments, the IDF has pounded Gaza with thousands of bombs, reducing some entire neighborhoods to rubble. The Economist estimated about a week ago (Oct 19) that
At least 4.3% of the enclave’s buildings appear to have been destroyed.
According to the maps included, most of the destruction was concentrated on specific areas, insofar closer to the Israeli border, like Beit Hanoun (pictured below).
UNITAR estimates building destruction/damage, which insofar have been focused on some specific areas (Deir al-Balah Governorate--which is south of the Israeli ordered evacuation area) put the number to under 2% in those. (UNITAR is notoriously famous for rather strict[er] standards as to what counts as destroyed.)
The "24 hrs" evacuation order for north Gaza [issued] on Oct 13 appears to have been some 2/3 successful, according to PBS with some 700,000 Palestinians moving south but 350,000 still remaining in the north, by Oct 26.
Also, virtually the entire strip appears to be without power, with the exception of some isolated buildings, according to satellite images taken at night, which recorded a 90% reduction in illumination.
And the IDF has launched some probing ground attacks (which some called them raids). That has yet to reveal what they'll ultimately settle for though.
For now they've also cut off all Internet to the region. (Those outages have been on and off though, since then.)
And it looks like the ground ops won't be limited to the North:
Defense Minister Yoav Gallant said Wednesday [Nov 15] the ground operation will eventually “include both the north and south. We will strike Hamas wherever it is.” Prime Minister Benjamin Netanyahu echoed the plans, saying Israel’s goal is “a complete victory over Hamas in the south and the return of our hostages.”
If Israeli troops move south, it is not clear where Gaza’s population can flee, with Egypt refusing a mass transfer onto its soil.