feat(app): migrate session interactions

[Brendonovich]

Summary

• route prompts, commands, forks, archival, and session controls through the compatible API
• migrate permission and question replies to current request contracts
• retain optimistic composer and session behavior

Validation

• bun typecheck in packages/app
• prompt submission and request dock tests

Stack

1. chore(app): vendor v2 promise client #38467
2. feat(app): add dual-server compatibility #38462
3. feat(app): support current event transport #38464
4. feat(app): project current server state #38459
5. feat(app): render current session timeline #38466
6. feat(app): migrate session interactions #38461 👈 current
7. feat(app): migrate discovery workflows #38465
8. feat(app): support current review data #38460
9. feat(app): support current pty transport #38463
10. fix(app): use current default model #38603