Pausing the scene tree stops the physics processing.
If true, the SceneTree is paused. Doing so will have the following behavior:
- 2D and 3D physics will be stopped. This includes signals and collision detection.
Popups are modal by default but I don't know if they stop the scene tree processing.
If they do then you needn't pause the scene tree.
If they don't they you will need to add a state machine to bypass processing while in the 'pause' state or something similar.