[1.0 UI] Permanent transport controls

This ticket tracks the implementation of the 1.0 implementation of the transport controls, where they are permanently in the same place on the screen, except:
- If covered by system UI like the file importer, the PIP window, fullscreen video, etc.

No files or tests are named. Start by locating the existing transport-control UI and run the app to observe its current placement; implement the permanent placement described in the issue and verify that system UI such as the file importer, PIP window, and fullscreen video can cover or replace it as specified.

Written by the indexing model from the issue text.