Think about your question, depending on the tool, Rust might not be needed, is high level memory performance and safety needed in a coding agent ? Probably not.
It's high speed iteration of release ? Might be needed, Interpreted or JIT compiled ? might be needed.
Without knowing all the requirements its just your workspace preference making your decision and not objectively the right tool for the job.
While not directly related to GP, I would guess that a codebase developped with a coding agent (I assume Claude code is used to work on itself) would benefit from a stricter type system (one important point of Rust)