Reddit reviews Door Knob Covers - 4 Pack - Child Safety Cover - Child Proof Doors by Jool Baby

Doorknob protector. Make sure that everything in his room is super baby proofed--don't forget to anchor all bureaus, dressers, shelves, everything--and then put a doorknob protector on the inside doorknob. If he gets out of bed, he gets out of bed, but you can sleep soundly knowing that he is safe. My kid got out of bed the first few nights and I actually found him asleep on the carpet surrounded by cars a couple times. Eventually he would just throw himself back in bed when he got tired, and from there he started staying all night. This is the one we use: https://www.amazon.com/Door-Knob-Covers-Child-Safety/dp/B071GWJX4D

You could also do one of those door knob covers that make it hard for little hands to turn the knob

Door Knob Covers - 4 Pack - Child Safety Cover - Child Proof Doors by Jool Baby https://www.amazon.com/dp/B071GWJX4D/ref=cm_sw_r_cp_api_i_PwiNDb9FYXH26

Get the door knob safety locks: Door Knob Covers - 4 Pack - Child Safety Solution - Child Proof Doors by Jool Baby https://www.amazon.com/dp/B071GWJX4D/ref=cm_sw_r_cp_api_-jRYzb6R34CMN

Don't tell him about them and when he tries doing it but can't, yell out "suckerrrrrr!"

How about doorknob covers?:

https://www.amazon.com/Door-Knob-Covers-Child-Safety/dp/B071GWJX4D

Maybe try those plastic covers for traditional door knobs. Not sure what your of shower / bath faucet you have but if it's two separate knobs they might work.
https://www.amazon.com/dp/B071GWJX4D/ref=cm_sw_r_sms_apa_i_v8Q2Db00HVCQK

If you have the right type of faucet this might be a solution. Good luck!

If you have round door knobs, use the clamshell guards like this.

Then wrap them with a layer of this.

That will make it so you need an adult amount of pressure to open the doors.

I've heard the doorknob blockers used for wandering children, most with disabilities work really well.

Stuff like that.