[Feature Request] Add Option to Save Incremental Plan Progress

Description
In plan mode (activated by shift+tab),
claude-code should offer another option to write down the plan, instead of starting coding or continue planning. It's often the case that the agentic loop of "plan -> code -> test" will run out of context quickly.

Unless we have setup an appropriate subagent to execute a plan, this scenario will occur quite frequently, especially with complex tasks and large codebase. Interrupting an agentic loop in the middle when context is running out is not necessarily better either.

An option to write down a plan should be given to the user to incentivize writing down incremental progress of a session. Loading a session from the history by resuming only loads the whole conversation in a session, it doesn't provide a granular recording.

Another option: Writing in memory is probably not suitable either, as we don't always need to load up all the written down plans and progress for each session.

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 1.0.117
• Feedback ID: 475aae6e-f4c3-4a72-a3ba-670e40bf3f3d

Errors

[{"error":"Error: Language not supported while highlighting code, falling back to markdown: \n    at Bz (/$bunfs/root/claude:1655:1192)\n    at <anonymous> (/$bunfs/root/claude:1655:2177)\n    at map (native:1:11)\n    at Bz (/$bunfs/root/claude:1655:2149)\n    at map (native:1:11)\n    at Bz (/$bunfs/root/claude:1655:2054)\n    at map (native:1:11)\n    at S7 (/$bunfs/root/claude:1655:905)\n    at n4W (/$bunfs/root/claude:3304:13729)\n    at aq (/$bunfs/root/claude:47:19415)","timestamp":"2025-09-17T08:41:23.778Z"},{"error":"Error: Language not supported while highlighting code, falling back to markdown: \n    at Bz (/$bunfs/root/claude:1655:1192)\n    at <anonymous> (/$bunfs/root/claude:1655:2177)\n    at map (native:1:11)\n    at Bz (/$bunfs/root/claude:1655:2149)\n    at map (native:1:11)\n    at Bz (/$bunfs/root/claude:1655:2054)\n    at map (native:1:11)\n    at S7 (/$bunfs/root/claude:1655:905)\n    at n4W (/$bunfs/root/claude:3304:13729)\n    at aq (/$bunfs/root/claude:47:19415)","timestamp":"2025-09-17T08:41:24.075Z"},{"error":"Error: Language not supported while highlighting code, falling back to markdown: \n    at Bz (/$bunfs/root/claude:1655:1192)\n    at <anonymous> (/$bunfs/root/claude:1655:2177)\n    at map (native:1:11)\n    at Bz (/$bunfs/root/claude:1655:2149)\n    at map (native:1:11)\n    at Bz (/$bunfs/root/claude:1655:2054)\n    at map (native:1:11)\n    at S7 (/$bunfs/root/claude:1655:905)\n    at bR0 (/$bunfs/root/claude:1803:41539)\n    at aq (/$bunfs/root/claude:47:19415)","timestamp":"2025-09-17T08:43:11.525Z"},{"error":"Error: Failed to fetch version from stable: Error: ECONNREFUSED\n    at TC9 (/$bunfs/root/claude:2875:16304)\n    at processTicksAndRejections (native:7:39)","timestamp":"2025-09-17T11:00:01.539Z"},{"error":"Error: Failed to fetch version from stable: Error: ECONNREFUSED\n    at TC9 (/$bunfs/root/claude:2875:16304)\n    at processTicksAndRejections (native:7:39)","timestamp":"2025-09-17T11:57:34.924Z"},{"error":"Error: Failed to fetch version from stable: AxiosError: timeout of 30000ms exceeded\n    at TC9 (/$bunfs/root/claude:2875:16304)\n    at processTicksAndRejections (native:7:39)","timestamp":"2025-09-18T02:28:47.072Z"},{"error":"Error: EISDIR: illegal operation on a directory, read\n    at readFileSync (unknown)\n    at GdG (/$bunfs/root/claude:3568:9434)\n    at call (/$bunfs/root/claude:1665:981)\n    at MT9 (/$bunfs/root/claude:3292:18664)\n    at processTicksAndRejections (native:7:39)","timestamp":"2025-09-18T03:05:16.707Z"}]