It’s common enough to use a booster pump for high end, multi head shower setups.... while using one for just a single shower head may not be the intent, long as the head (and related piping) can handle the pressure and flow, no reason why it wouldn’t work.
https://www.amazon.com/KOLERFLO-Pressure-Booster-Automatic-H15GR-15/dp/B07J43CWC3
As for the faucets and such; that you’ll probably have to learn to live with.