I'm using

Modifier.selectable(...)

and when the composable is clicked, the animation plays and UI is updated, but the composable doesn't stay selected (graphically speaking). Do I have to change the background colour myself?

yes, you need to update the background color in according to your state. The selectable modifier just provides the callbacks and sets the accessibility/debug properties

It's a little weird that the background colour changes for the animation though.

can you share a code snippet?

You should use

selectedRoom == room.id

to define the UI. The composable reflects the state and you are the owner of that state