If prompts are specifications for a change of the system's behavior, then it seems natural to manage them as changes and not as resources.
This would also keep them in the right "historical context" of the repo and avoid the "prompt rot" you were talking about.
Functional safety development processes often demand code-review, technical design decisions, changes of plans, or intentional compromises; to be linked together with reference IDs in the code they effect. But the workflow for this is usually extremely manual and absolute misery. But a codebase made like this is like magic to read later.
You'd consequently only need to implement your custom git gui and extension to visualize this information.
Maybe a good project for the next weekend? Just eg make a prototype tui in golang and see where you end up