v1.16: tower: when syncing from vote state, update last_vote (backport of #32944)

[mergify]

This is an automatic backport of pull request #32944 done by Mergify.
Cherry-pick of 329c6f1 has failed:

On branch mergify/bp/v1.16/pr-32944
Your branch is up to date with 'origin/v1.16'.

You are currently cherry-picking commit 329c6f131b.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Changes to be committed:
	modified:   core/src/consensus.rs
	modified:   core/src/replay_stage.rs

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   programs/vote/src/vote_state/mod.rs

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/github/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

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[codecov]

Codecov Report

Merging #32960 (ce505b9) into v1.16 (45dbe2b) will increase coverage by 0.0%.
The diff coverage is 91.3%.

@@           Coverage Diff           @@
##            v1.16   #32960   +/-   ##
=======================================
  Coverage    81.9%    81.9%           
=======================================
  Files         762      762           
  Lines      208003   208055   +52     
=======================================
+ Hits       170465   170549   +84     
+ Misses      37538    37506   -32