[clang-tools-extra] [run-clang-tidy.py] Refactor, add progress indicator, add type hints (PR #89490)

[Nicolas van Kempen via cfe-commits]

nicovank wrote:

Rebased on top of cc54129b983799e1aaea77aa0ff3040dc30cbc8c.

Ping @PiotrZSL, what to do here? I can keep the current flush and separate stdout/stderr behavior in this PR, it can be changed later.
But I don't think flushing fixes that issue of mis-ordered output lines, IMO either 1. use the same stream to force order 2. let user unbuffer with the `python3 -u` flag.

https://github.com/llvm/llvm-project/pull/89490