Build cache: cheap sub-project detection and resilient global mount

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