So the challenge is if you call the in-house maintenance team and they can’t fix it then they’ll charge you to have a real plumber come out? So the alternative is just not to use the sink?

Is the blockage complete or partial? Like, does the water go down eventually or never?

I wrote the entire below section before I thought of an even easier approach. Easy approach: get yourself one of these plastic drain snakes. They’re cheap and effective. Your local big boss hardware store will have them, too. If you can’t clear it with one of these it is probably serious and I would hold off on reporting it.

Slightly less easy method (since I already typed it):

Another commenter mentioned removing the p-trap. This really is a trivial process requiring nothing but a bucket to catch any water that is remaining in the sink. Just unscrew the rings on each end and remove. Take not of how much effort it takes to remove them because that’s how tight you’ll want to make it when you reassemble. There may be bevelled rings on each end. Watch that you put them back on in the same direction (assuming they’re bevelled in one direction).

Once removed, shake it out over the garbage (not the sink, that’d be dumb… ask me how I know) and whatever is causing the issue will probably fall into the trash. You might have to shove something in there to loosen it if things got really bad. If there’s broken glass in there be very careful! You don’t want to cut yourself covered in dirty sink water. Put it all back together and if it still doesn’t drain you have your answer: will probably be expensive and you will want to delay reporting it until you can afford the bill.