Shortcut: submit prompt and go to the next Done thread

[Gavin-Key]

I'd like a configurable shortcut that sends the current prompt and opens the next Done thread in the sidebar.

When running several agents, this would let me review a finished response, send a follow-up, and move straight to the next one. If nothing else is Done, stay in the current thread. Also stay if sending fails.

[lukemavdynamics]

I'd like this too, and I'd suggest one variant: make it an automatic opt-in setting alongside the Working section beta, rather than only a shortcut.

With the Working section on, the inbox already holds only threads that aren't working, so its top row is the next thread that needs you. A setting, maybe "Move on after sending", would open that thread whenever a send starts the open thread working. If the inbox is empty, it would open a new thread in the same project, the way mod+alt+enter (#15050) does. That differs from your "stay" fallback, and I'm happy with either.

Details I'd suggest:

• It only moves after the server accepts the turn, so a failed send keeps you on the thread with the error.
• Steering or queueing into a thread that's already running doesn't move you.
• Pinned threads aren't targets, only the inbox.
• Web and desktop only. Mobile has its own navigation.

Related: #15408 asks for the same forward step after settling, and #16090 for the settle shortcut. #13926 added the Working section and deliberately keeps the open thread visible in it.

I have a small worked implementation on a fork (about 120 lines including a user-doc paragraph, off by default): lukemavdynamics/t3code@aa8c666...feat/working-section-advance. If the direction sounds right, as a shortcut, a setting, or both, I'm happy to open it upstream at whatever scope you prefer.