Tesla charge ports are latched onto by the car, so when they get stuck it's because the car won't let go. You can access a manual release from within the trunk but it is by no means easy, convenient, or well-known.
That being said, I've had this happen exactly once 3 years ago. All the complaints I've seen are around the 2018 time frame which is when I had issues so I wonder if it was a software issue with the Model 3 that's since been resolved.
> Everything I've seen using CCS, "stuck" is because someone forgot to push the trigger twice to unlock both the car and charger side.
Trigger? With CCS there's usually a button which is just one side of a lever with a latch at the other end. It's purely mechanical and you have to hold it down to release.