So I too thought that stuff was broken when I hit a similar issue years ago.
However, it's not.
Not only does each container have a finite amount of space so does the room.
So sometimes someone will load up the floor or a table and it will then cause the room to fill up.
So it's not just that your locker is filled, it's that someone else might have piled enough somewhere else to hit the room maximum.
A test for this is to try and just drop the thing in the room if it says something like "there is no more room for that" it means there is generally too much shit in that room and you need to get rid or reorganize it to another area.
This happens in crafting halls a lot and in barracks that people stockpile shit in.
This is I believe this way to stop folks from just putting seven hundred chests in a room and turning it into an endless treasure trove.
Icly I would recommend you talk to your leaders and clean some shit up or sell it off to Indy folks.
I It's definitely the case that sometimes you can still put stuff in containers but not be able to drop anything because the room is "full." I thought this was because containers occupy space in the room equal to their maximum capacity by default, and so adding removing items from a container shouldn't affect the room's overall capacity. Is that not how it's supposed to work?
Sometimes it's the container hitting capacity, but other times it's the room capacity.
Just like you might not be able to stick a long bone length in a large bag, but you'll be able to put three slabs of meat in it.
When the room hits capacity though, you can't do anything but subtract from the items.
There's a difference between rigid containers and flexible containers. A rigid container (like a chest) will always add its max capacity to the room capacity. A flexible container (like a bag) will only add its current capacity. If the room is at capacity, you can't put anything anywhere, including being unable to put a flexible container into a rigid container even if it'll fit.
A workaround is to toss one of those flexible containers into another room. You'll then be able to put things into the rigid container. Then you should think about getting rid of things sitting out in the room, because it's extremely annoying to have to move things out of the room every time you want to use your footlocker.
Edit to add: you can 'assess' a container to see if it's full