Bathroom Light Fixture: What is this? And where can I get a replacement?
There's no standard for this type of twist'n'lock and no reason for manufacturers to adopt one, so your best bet is to find a brand name or a label somewhere, probably hidden inside the part of the fixture that is mounted the wall.

IKEA has a similar fixture but it is unlikely to be compatible. Still useful if you want to change both.

Make sure you follow code and pick the proper fixture for your bathroom. Check if there is an Earth wire coming out of the wall before you buy the light! If there is no Earth you need a light that does not require Earth (Class II). Here the fixture type depends on distance from bathtub/shower.

Note this type of closed splash-proof bathroom fixture has no airflow which tends to cook LED bulbs and reduce their life if left on continuously. Shouldn't be a problem in a bathroom though, it isn't supposed to stay lit 24/7.