[FEATURE]: Multiple chat tabs per session in web/desktop

[notkainoa]

Feature hasn't been suggested before.

• [x] I have verified this feature I'm about to request hasn't been suggested before.

Describe the enhancement you want to request

It would be very helpful to have multiple chat tabs within a session in the web view and desktop app, similar to how conductor.build handles it:

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This would allow:

• Parallel exploration of different ideas or tasks within the same worktree/session

• Easy context switching without spawning entirely new sessions

• Cleaner organization for complex workflows that branch into sub‑threads

A simple tab bar UI for each session, with keyboard shortcuts to create, close, and switch tabs, would make it much easier to manage multi‑step work.