This is an automated cherry-pick of #18236

What is changed and how it works?

Issue Number: Close #18233

What's Changed:

In previous work #16239, we introduced the busy_on_apply state to indicate
whether a Peer is pending the application of pending Raft logs upon restart.

However, this approach misses a corner case: if the Peer quickly enters the
hibernate state after restarting, the busy_on_apply state may not be updated
in a timely manner. This results in the Node failed to update the count of pending
applying regions, continuously reporting an incorrect is_busy == true state to PD.
Consequently, this can slow down the rolling-restart progress more than expected.

Therefore, this PR addresses this issue by updating the applied state in on_apply_res.

Fix the bug where some hibernated peers, marked with `busy_on_apply == true`, 
cannot be reset with normal even thought the `applied_index == committed_index`.

Related changes

• PR to update pingcap/docs/pingcap/docs-cn:
• Need to cherry-pick to the release branch

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No code

Side effects

• Performance regression: Consumes more CPU
• Performance regression: Consumes more Memory
• Breaking backward compatibility

Release note

Fix the bug where some hibernated peers, marked with `busy_on_apply == true`, 
cannot be reset with normal even thought the `applied_index == committed_index`.