Compilers don't usually write the code that ends up in a PR. But compilers do (and should) generally leave behind some metadata in the end result saying what tools were used, see for example the .comment section in ELF binaries.

Are you checking in compiled artifacts? Then yeah, we should have a chain of where that binary blob came from.

Do you check in binaries into your git history? If so, you should mark a commit as generated, and the commit message (plus repository state) should be enough to recreate it 1:1.

Similarly, if I use e.g. jextract or uniffi to generate Java interfaces from C code and check that in, I'll create tooling to automatically run those, and the commit will be attributed to that tooling.

Compiler versions are usually included in the package manifest. Generally you include commit info compiler version and compilation date and platform embedded in the binaries that compilers produce.