[llvm] Add thread-local overrides for `llvm::errs()` and `llvm::outs()`. (PR #90374)

[Alexandre Ganea via llvm-commits]

aganea wrote:

What I had in mind is this: https://github.com/aganea/llvm-project/commit/a17991eb07e5a50ad1cb51b2db713b67f641f1d4

The general idea here is to extract all statics into the `ToolContext` which we already have. We could do that progresively, but here your override needs is a good opportunity to start somewhere.

https://github.com/llvm/llvm-project/pull/90374