fix(app): clear stale todo dock items on submit

[Joeyzzyy]

Issue for this PR

Closes#20586

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

This fixes a session todo dock bug where stale todo items from an earlier turn could remain visible above the input after the user submitted a new prompt.

The app was already clearing todos on abort, but not on the normal submit path. That meant old todo dock items could stay visible until a fresh todo update arrived for the new turn.

This change clears the current session todo state immediately when a new turn is submitted, so the next request starts from a clean todo dock state instead of reusing stale tasks.

How did you verify your code works?

• added a focused regression test for clearing stale todos before sending a followup prompt
• ran bun test src/components/prompt-input/submit.test.ts from packages/app
• ran bun typecheck from packages/app

Screenshots / recordings

Not included. This is a small session-state behavior fix.

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR
• I have updated relevant tests if needed

[Joeyzzyy]

Closing this to focus review on the smaller prompt-history search change in #21253.