If the door protect stops the galvo, the door switch seems obviously correct. If your setup is like mine, you can look at the “Port and Laser Settings” page of your Device Settings and verify by watching the IP Ports red/green indicator for the port selected for “Door Protect”. If it changes state based on the door, you’re good.
The door interlock is generally connected to one of the very few available inputs on one of the connectors on the controller board. The galvo head is connected to a second connector. The laser source is connected to a third connector.
If your laser source remains active when the machine is paused, that would seem like it would have to be an issue with the controller or its connection on that third physical DB(some number) port. I know of no configuration options available in LightBurn that could cause such an issue, but I did see a similar-ish post a while back about that port and undesired lasering: