Every restart of Premiere Pro forgets about playback on the secondary monitor. The checkbox is there, but one needs to click/unclick it for the image to show up on the second screen.
Steps to reproduce:
1. Edit > Preferences > Playback > Transmit Device Playback -- Select secondary monitor from the list of available monitors
2. Press OK
3. Everything is as expected - image appears on the secondary monitor
4. Exit/Close Premier
5. Restart Premier
6. Re-open the project
7. Secondary monitor is not activated
8. Edit > Preferences > Playback > Transmit Device Playback -- see the checkbox being there -- Uncheckbox it
9. Contrary to the uncheck status, you'll see the playback working on the second screen
10. Save and exit
11. Go to step 1
System info
Application: Premiere Pro (Beta) v25.6.0.59
OS: Windows v10.0.19045, RAM: 63.93 GB, CPUs (logical): 8