Auto merge of #146592 - Kobzol:tidy-diag, r=jieyouxu

Implement a simple diagnostic system for tidy

In https://github.com/rust-lang/rust/pull/146316 and https://github.com/rust-lang/rust/pull/146580, contributors independently wanted to reduce the verbose output of tidy. But before, the output was quite ad-hoc, so it was not easy to control it.

In this PR, I implemented a simple diagnostic system for tidy, which allows us to:
1) Only print certain information in verbose mode (`-v`)
2) Associate each (error) output to a specific check, so that it is easier to find out what exactly has failed and which check you might want to examine (not fully done, there are some random `println`s left, but most output should be scoped to a specific check)
3) Print output with colors, based on the message level (message, warning, error)
4) Show the start/end execution of each check in verbose mode, for better progress indication

Failure output:
<img width="1134" height="157" alt="image" src="https://github.com/user-attachments/assets/578a9302-e1c2-47e5-9370-a3556c49d9fc" />

Success output:
<img width="388" height="113" alt="image" src="https://github.com/user-attachments/assets/cf27faf8-3d8b-49e3-88d0-fac27a9c36a8" />

Verbose output (shortened):
<img width="380" height="158" alt="image" src="https://github.com/user-attachments/assets/ce7102b8-c2f3-42a8-a2ec-ca30389be91e" />

CC `@nnethercote` `@RalfJung` `@GuillaumeGomez`

The first two commits and the last commit are interesting, the rest is just mechanical port of the code from `bad: &mut bool` to `DiagCtx` and `RunningCheck`.

The `extra_checks` check could be further split, but I'd leave that for another PR.

r? `@jieyouxu`

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