Reproduction steps:
1. Open the attached “BugRepro” project
2. Open “Scenes/SampleScene” Scene in the Project window
3. Enter Play Mode
4. Focus the mouse cursor in the Game View (cursor should disappear)
5. Press the “E” key
6. Observe the Game View

Expected result: The mouse cursor remains locked (hidden)
Actual result: The mouse cursor is unlocked (visible)

Reproducible with: 2021.3.41f1, 2022.3.39f1, 6000.0.12f1

Reproducible on: Ubuntu 24.04, Ubuntu 22.04 (user)
Not reproducible on: Windows 10

UPDATE:
This issue is caused because GTK dispatches a 'focus-out-event` signal when the ProgressDialog is displayed resulting in GameView releasing CursorLock. This behavior appears specific to X11 and/or GNOME window manager, in which the top-most window always has keyboard focus. It's not something we can reasonably change.

However, a work-around fix may still be possible.