He, and many others, actually does seem to have the support of a lot of the party. Liz Truss didn't - she just had the support of the current party leadership.
This is pretty much the exact opposite of true – Truss had the support of the membership, and did not have the support of the "leadership" or the parliamentary party. Sunak was the other way round.
At the same time, they did just have an election, so it's not like they are going to be interested in having another one
There's not really another choice, though it's possible that only one candidate will stand, in which case an election is avoided.
Labour-aligned folks are calling for one for obvious reasons.
They're calling for a general election, not a Conservative leadership election.