Reddit mentions of Highlander 20 Litre Solar Heated Camping Shower

Dude that's awesome... making a mental note of your ideas! Especially the LED projector. Excellent.

Hot water might prove pretty damn challenging as it's a massive electrical power demand. If this is a summer camper, building a curved hot water tank into the roof with black paint like a solar shower might do the trick on a sunny day, but it won't work when the sun's not out.

On boats, we typically use some of the waste engine heat to warm a hot water tank for free, it's a shame there's no way to do that with a road vehicle (it would work for a full-time RV where the plumbing is permanent but not for something being hitched + unhitched so far back from the engine block).

To be honest, cold running water plus a small gas stove with a kettle is probably the only practical way to do this. Gas has the ridiculous energy density you need. Batteries don't. And without a shower, do you ever actually need more than a camping kettle's worth of hot water?

Side note: a water pressure pump may actually be a bad idea. OP is pretty heavily limited on the water tank capacity. It turns out (again, know this from boat design) that fitting pressurised water increases consumption many times more than just having taps with foot-pump action. We are naturally far more careful to only use what we need when pumping by hand!