Its nothing to do with your wet room but your drain seems clogged. You should get it open
by reporting it to in house service and it should never happen again. And
remember to get some acid cleaning liquid from nearby shop and pour that in every
week to avoid it clogged again. If this don’t help then the wet room is poorly
fitted or is of bad quality. Therefore many good bathroom retailers like Royal
Bathrooms who sell good quality wetrooms. But since it is managed by university
and you are into a temporary residence, nothing like that can be done. The best
way to deal is to avoid your drain pipe getting clogged. The best liquid if you
want to unclog it as DIY is sulphuric acid but not widely available and needs to
be very careful while using it. Use glasses and gloves and avoid direct contact
with it.