"Is this a shape button timed for the rest of the project, on the first slide? I can see that it is not on the master slide."
It is! I guess I need a new Master for the slides that contain video, and place the button there.
That is the problem with those 'basic' videos, they always miss explaining the 'why'.
The option 'Continue playing the project' is only necessary when you have a pausing point, but don't want to release the playhead, it should remain at that pausing point. Typical example: when you have a dashboard with several items to be clicked, and those items all have the same pausing point you have to uncheck that option. That way the user will be able to click all the clickable items, since the playhead will not move, but remains at the same frame, which will be the last frame of the active part of the clickable items. If you check Continue... the user would be able only to click one item, because the playhead would be released and then will be in in the inactive part for all the clickable items.
In this case you need to have no pausing point, and the project flow should be normal since you don't want the user to click a Continue button as well. An example of a toggle button can be to open/close a TOC in overlay: while being open, you don't want the project to continue so you'll uncheck Continue playing the project. But when closing the TOC project should continue playing. In that case you need a conditional action, it will not work with your simple action Toggle cpCmndTOCVisible.