[clang-tools-extra] [clang-tidy] Create bugprone-public-enable-shared-from-this check (PR #102299)

[Piotr Zegar via cfe-commits]

https://github.com/PiotrZSL requested changes to this pull request.

I'm fine with idea behind this check. Just few fixes are needed.

https://github.com/llvm/llvm-project/pull/102299