v1.14: 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/v1.14/pr-32944
Your branch is up to date with 'origin/v1.14'.

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/replay_stage.rs

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   core/src/consensus.rs
	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 #32959 (b96790a) into v1.14 (f717db6) will increase coverage by 0.0%.
The diff coverage is 90.7%.

@@           Coverage Diff           @@
##            v1.14   #32959   +/-   ##
=======================================
  Coverage    82.1%    82.1%           
=======================================
  Files         665      665           
  Lines      185541   185595   +54     
=======================================
+ Hits       152474   152538   +64     
+ Misses      33067    33057   -10