To fix your Xbox One controller trigger being stuck, you will need to pry open the casing and clean the trigger contact pad sticking to the trigger.
You can use rubbing alcohol on a Q-tip to clean the contact pad and the opposite end of the trigger that will come in contact with the pad. The pad is there as a shock absorber so the trigger doesn’t slam into the plastic frame of the controller constantly. Many times, it’s sticking because the pad has completely deteriorated and the glue left from the pad is sticking to the trigger. You can also replace it with any felt-like material that will act as a shock absorber.
See this tutorial for more details on how to open the plastic panel to the controller. You can actually use your finger nails instead of a plastic pry bar as its safer to do so with your bare hands rather than scuffing your controller case.