Server: refine Server(proxy state machine)

## Bug Report

See https://github.com/pingcap/tiflash/issues/9855

Make easy for cherry-pick.

Please answer these questions before submitting your issue. Thanks!

### 1. Minimal reproduce step (Required)



### 2. What did you expect to see? (Required)

### 3. What did you see instead (Required)

### 4. What is your TiFlash version? (Required)