For the purpose of disclosure, it should say “Warning: AI generated code” in the commit message, not an advertisement for a specific product. You would never accept any of your other tools injecting themselves into a commit message like that.
I don’t think that’s necessarily the case. Exposure and discovery aren’t that tightly correlated. Maybe there’s a small effect, but I think it is outweighed by the fact that blast radius and spread is reduced while buying time for discovery.