[Feature Request] Implement background compaction with bridging to eliminate user-facing lag during context window compaction

Bug Description
Re: Long and painful lag around Compaction... It seems to me that if the compaction window is set early (like the 200K I use, or the 400K Boris Cherny seems to suggest), then there's plenty of buffer up to the 1M context window limit.

So, one option is to let the current task continue, start compaction behind the scenes, and then do a quick second round of bridging between when the compaction started and wherever the user currently is... Possibly by just appending the user inputs or activity since, if it's not too long.

That way, the user doesn't need to feel that compaction occurred and work doesn't get slowed down.

Environment Info

• Platform: darwin
• Terminal: ghostty
• Version: 2.1.101
• Feedback ID: d4fa3baa-0a15-4e86-824b-6a7c8389dd91