[FEATURE] Allow plan mode to sync plan to a file

Plan mode is an integral part of my workflow. One thing I do is I write the plan to a markdown file throughout the planning process. I do this for multiple reasons:

1. If CC crashes or I close it accidentally. I know I can resume if this happens, at least I can if the history files weren't corrupted.
2. If I want to reference the plan from multiple agents.
3. I commit the plan along with my code, at least during development as I want to preserve the plan along with my code. It's not a part of the MR I publish.

The challenge right now is I have to switch to a different mode in order to write the file. That isn't terrible but it's inconvenient and I have to remember to do it. The real inconvenience is that CC will sometimes think that by switching out of plan mode I'm ready to implement so it takes off making changes when I'm not ready for it to do so.

A function of plan mode to write to a file and also sync changes would be a great addition. Thank you.