Use new queued prompt panel for /compact-and and /fork-and-compact

[harryalbert]

Description

Linked Issue

• The linked issue is labeled ready-to-spec or ready-to-implement.
• Where appropriate, screenshots or a short video of the implementation are included below (especially for user-visible or UI changes).

Testing

• I have manually tested my changes locally with ./script/run

Screenshots / Videos

Agent Mode

• Warp Agent Mode - This PR was created via Warp's AI Agent Mode

[harryalbert]

Warning

This pull request is not mergeable via GitHub because a downstack PR is open. Once all requirements are satisfied, merge this PR as a stack on Graphite.
Learn more

• Use new queued prompt panel for /compact-and and /fork-and-compact #11575 👈 (View in Graphite)
• Use new queued prompt UI for cloud mode #11547
• Create new queued prompts list UI #11439
• master

This stack of pull requests is managed by Graphite. Learn more about stacking.