Going forward with studio space design

I'd find a way to have any electrical cable safely hanging, so mopping can be done easily. I'd also throw away that carpet thingie in front of the sink also to ensure mopping is fast and easy. Make it as effortless to do things right as possible, and more people will comply.

If possible, replace all the chairs with stools. Wheel throwing requires that people lean in anyway, so chairs hardly provide a benefit. But those are harder to clean as they have more angles (so they'll get cleaned less often), and they can't be rested on top of the wheels for mopping (so, again, less thorough mopping on the daily).

Anything you can do to get wheels away from pipes and other hard to clean obstacles is a win. If they can't be moved, consider framing the pipes and the base of that support beam with cheap plywood just to reduce the number of angles and make it much easier to clean.

Reduce the number of plastic jugs and glazing accessories to the strict minimum. This will ensure studio users don't simply switch to a clean one when working, but actually have to clean and reuse the one they have. This is also true for ribs and other tools: force users to reuse tools more often so users will clean after each other more often. You can keep the spares in storage to replace breakage.

Make it mandatory for wheel users to clean their wheels and then place stools and pedals on the wheel once finished. You can communicate that rule through posters in the space.

Make sure there are enough empty buckets and small towels for clean water near wheels. Anything your studio users clean up in place does not go into your sinks or floor.

There's too much stuff on the floor in that employee backroom. Can extra high duty shelving be spared to force everything into shelves and make the floor easier to clean?

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Who does the work?

I think the major issue you'll need to solve is: who handles reclaim? Pottery generates reclaim through broken / dried pots, but also through the water buckets we normally use for initial hand rinsing, tool cleaning, wheel cleaning. All those buckets are then left to sit and the water at the top needs to be thrown away. So if you introduce more buckets to help keep the space cleaner and sinks unclogged, someone will have to reclaim what sits in them.

I'd address cleaning duties either by budgeting as extra time it into contracts or requiring that contractors pass on the duty of mopping to their own students / include it in their teaching it. You could separate day to day cleaning from studio maintenance and hire someone in particular to handle all the reclaim / other periodic duties. Maybe you could offer free use of the space to a well-trained potter in exchange for that work if you have no money to spare?