CI: Add manual pre-commit hook for clang-tidy

[Repiteo]

Supersedes #90219

Implements a manual hook for clang-tidy, allowing one to utilize clang-tidy without needing separate downloads beyond pre-commit itself. The reason for specifying that it's a "manual" hook is because this type of hook is not automatically invoked; instead, it must be called directly via pre-commit run --hook-stage manual clang-tidy (a comment was added to .pre-commit-config.yaml explaining this). This integration rendered misc/scripts/clang_tidy.sh redundant, so it's been removed.

Additionally, the .clang-tidy file has been given modernized yaml syntax. CheckOptions functions like an implicit dictionary, not needing nearly as many bounding quotes; the only options present are the ones that we've explicitly changed. Checks has been transformed into a multi-line string, making future changes much more obvious for version control. HeaderFileExtensions and ImplementationFileExtensions were added to specify the checked extension types in .pre-commit-config.yaml. FormatStyle was changed to file, so there no longer needs to be a second-pass of clang-format. HeaderFilterRegex was changed to an anti-pattern excluding the thirdparty folder; can be simplified to utilize ExcludeHeaderFilterRegex once v19 is released.

[akien-mga]

Looks great!

[akien-mga]

Thanks!