CI: Update clang-format to 22.1.3

[RytoEX]

Description

CI: Update clang-format to 22.1.3

Additionally, use the .clang-format file from obs-studio and apply the changes.

Motivation and Context

Recently updated GitHub Actions on obs-websocket. Wanted to do the same here, but realized that clang-format also needed to be updated, so let's do that.

How Has This Been Tested?

I haven't done a build/runtime test because this should just be formatting changes.

Types of changes

• Code cleanup (non-breaking change which makes code smaller or more readable)

Checklist:

• I have read the contributing document.
• My code has been run through clang-format.
• My code follows the project's style guidelines
• My code is not on the master branch.
• My code has been tested.
• All commit messages are properly formatted and commits squashed where appropriate.
• I have included updates to all appropriate documentation.