fix: Capture session ID from stream headers rather than final event

[BinaryMuse]

This allows us to ensure a cancelled request still gets its session ID set on the client, allowing the user to resume the conversation from the cut-off point.

[greptile-apps]

Greptile Summary

This PR captures the AI server session ID earlier in the streaming flow. The main changes are:

• Adds a SessionIdentity stream frame from x-atuin-ai-session-id response headers.
• Converts that frame into a new FSM SessionIdReceived event.
• Stores the header-provided session ID before the final done SSE event arrives.

Confidence Score: 3/5

This should be fixed before merging.

• Cancelled streams can still lose the session ID after process exit.
• Empty header values can poison the stored session ID.
• Existing sessions can keep stale IDs when the server returns a replacement in headers.

crates/atuin-ai/src/fsm/mod.rs

Important Files Changed

Filename	Overview
crates/atuin-ai/src/fsm/mod.rs	Stores session IDs from the new header event, but misses persistence and validation cases.
crates/atuin-ai/src/stream.rs	Emits the new session identity frame from successful stream response headers.

_{Reviews (1): Last reviewed commit: "fix: Capture session ID from stream head..." | Re-trigger Greptile}

[BinaryMuse]

@ellie I think we're probably fine with those caveats but open to thoughts.

[ellie]

ya i think those caveats are fine! tyty