It is some form of marking, and neutered rabbits can absolutely mark if they feel there is need. My two neutered boys made poop-barriers along the gate that separated them (they weren’t bonded). They sometimes peed. Now one of the rabbits is gone, the other one isn’t marking anymore, even though the gate is still there.
So it seems for some reason, your bun is marking territory. It could be a response to your marking your territory by closing the door. It’s instinctive with your bun of course.
The best thing would probably be to not let him have access to the door. Sometimes a bunny forgets about things if you block them from accessing them for some time. One spring my Bam had a relapse in peeing on the sofa, I blocked the sofa off for a couple of weeks, and after that, Bam had just forgotten about it. Your room seems to have become extra desireable, perhaps because there’s a bed, buns love hiding under beds, it’s like a perfect burrow. Does he have hidey-houses in his own territory?
You should of course clean the area outside the door, first with detergent, then with vinegar and water.
You could bunny-proof the wires in your bedroom and let him hide under the bed. My bridge bunny did a lot of his daytime resting under my bed. Then he slept in it during the night, at the foot end. It can of course be a bit impractical.