Automatic merge from submit-queue (batch tested with PRs 59214, 65330). If you want to cherry-pick this change to another branch, please follow the instructions <a href="https://github.com/kubernetes/community/blob/master/contributors/devel/cherry-picks.md">here</a>.
Migrate cpumanager to use checkpointing manager
**What this PR does / why we need it**:
This PR migrates `cpumanager` to use new kubelet level node checkpointing feature (#56040) to decrease code redundancy and improve consistency.
**Which issue(s) this PR fixes**:
Fixes#58339
**Notes**:
At point of submitting PR the most straightforward approach was used - `state_checkpoint` implementation of `State` interface was added. However, with checkpointing implementation there might be no point to keep `State` interface and just use single implementation with checkpoint backend and in case of different backend than filestore needed just supply `cpumanager` with custom `CheckpointManager` implementation.
/kind feature
/sig node
cc @flyingcougar @ConnorDoyle
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