Model switch regression: switching back to a profile doesn’t reapply model (reasoning stays off), selector shows correct profile

[hannesrudolph]

Description

After switching between two models, switching back to the previously selected model does not apply. The selector shows Model A, but responses continue as if the previous model is still active.

Steps to Reproduce

1. Select Model A (has reasoning). Ask: "Tell me a joke."
   Expected: Reasoning is visible in the UI.
   Actual: Reasoning is visible.

2. Ask again: "Tell me a joke."
   Expected: Reasoning is visible.
   Actual: Reasoning is visible.

3. Switch to Model B (no reasoning). Ask: "Tell me a joke."
   Expected: No reasoning is shown.
   Actual: No reasoning is shown.

4. Ask again: "Tell me a joke."
   Expected: No reasoning is shown.
   Actual: No reasoning is shown.

5. Switch back to Model A. Ask: "Tell me a joke."
   Expected: Reasoning is visible.
   Actual: No reasoning is shown even though the selector shows Model A.

[roomote]

I'm exploring a potential fix for this model switching regression and will open a PR to share progress. The technical investigation in the issue description is very helpful - I'll implement Option A (updating task.apiConfiguration after rebuild) as it appears to be the simplest and most backward-compatible solution.

[roomote]

Opened a PR with my attempt at addressing this issue: #9180. Feedback welcome!