[Interactive Beam] Fix caching deadlock, wait race conditions, and stale graph in notebooks - #39161

Failed to save: Unable to reserve cache with key tox-Linux-py3.14-3a5e20ae55fb504d86457aca440cae6b5ce2e3e4f505442e81f298f7aec4a55e-6847b4ccd0ed907d087420d34a421a370283ecc6ae022be8f24d2506c5bb70fa. More details: cache write denied: token has no writable scopes

Cache reservation failed: cache write denied: token has no writable scopes

Cache reservation failed: cache write denied: token has no writable scopes

Cache reservation failed: cache write denied: token has no writable scopes

Cache reservation failed: cache write denied: token has no writable scopes

Cache reservation failed: cache write denied: token has no writable scopes