bwya77/DockAnchor — reverse-engineered prompt

Build me a lightweight native macOS app called DockAnchor for people using multiple monitors who are tired of the Dock jumping to the wrong screen. I want the app to let the user pick one display as the anchor, start protection, and keep the Dock from moving to other displays when the mouse hits the bottom edge.

It should run quietly in the background, have a simple main window that visually shows connected monitors, and update when monitors are plugged in, removed, or rearranged. Add a menu bar icon with quick status and controls, plus settings for start at login, run in background, show or hide the Dock icon, light or dark theme, and automatic updates.

Please include profiles so users can switch setups, and allow automatic profile switching based on connected displays. If the chosen monitor disappears, fall back to the primary or built in display. Make sure the app asks for accessibility permissions clearly, since it needs them to monitor and block the Dock movement.