You can use the free version (no need to pay), and it should be possible to drive Resolve using the Python API -- see this MCP server built on top of that API:
replyhttps://github.com/mhadifilms/dvr/
You can also try pointing Claude to the API surface directly.
The result might be chaotic, but you should be able to automate editing... maybe. :-) Ha. (You'd need a good loop to make sure Claude can see what it's doing..? Beyond screenshots I mean - ie how would Claude know its doing a good job editing?)