[YaokunLee]

Problem

The Paste Bar can fail to appear over another application’s native full-screen Space. With a left or right Dock, the bar also leaves an unused horizontal strip because its frame is based entirely on NSScreen.visibleFrame.

Changes

• Create the bar as a nonactivating panel and allow it to join other applications’ full-screen spaces.
• Make the panel key without explicitly activating Pesty, avoiding a switch away from the current full-screen app.
• Use the display’s full horizontal bounds while preserving the visible vertical bounds, including during resizing.

Validation

• swift test: all 7 existing tests pass.
• Universal release build succeeds for Apple Silicon and Intel.
• Local macOS 15.7.7 user testing confirmed the bar appears over full-screen Codex after the panel change.
• The subsequent side-Dock width correction builds successfully; visual confirmation of that final adjustment is still pending.

No clipboard screenshots are attached because the available reproduction image contains private clipboard contents. The visual change is that the bar extends to both horizontal display edges when the Dock is on either side.