Auto merge of #153560 - Shunpoco:decompose-extra-checks, r=lolbinarycat,kobzol

Introduce granular tidy_ctx's check in extra_checks

## Changes
This PR does:
- Extract sub checks in extra_checks to each function which takes a reference of TidyCtx
- Also extract python/npm dependency install steps to functions. They also calls tidy_ctx.start_check() 

The changes introduce some benefits:
- A failure on one sub-check doesn't stop other sub-check (except py/npm install functions. Because some sub-checks rely on them)
- A failure on a sub-check is tracked on TidyCtx's error check

Verbose output (shortened):
<img width="904" height="1251" alt="image" src="https://github.com/user-attachments/assets/53df4029-a820-467e-b849-ac05c02b396e" />

## Question
I considered that I would decompose each sub-check more so that main.rs calls sub-checks directly and those sub-checks are executed concurrently. But to do so, I think
1. main.rs has to know some implementation details of extra_checks (for example, it might need to know ExtraCheckArg to decide which sub-checks should be called or not), and/or
2. we should decompose extra_checks/ dir to utilize check! macro for sub-checks.

I'd like to know your opinion/suggestion.

Author: bors