The right way is some sort of inline water flow sensor, so it'll trigger within seconds of you turning on the shower to warm it up. With an esp32 and a sensor, and some clever use of the sleep function, it'd probably last a year or so on a couple of AA's.

Low effort and price tech is probably better in a wet environment though! If you just want the mood lighting, get a wireless button and stick it somewhere near. Tap it on, tap it off!

If you want to feel that automatic magic, consider a cheap battery powered temperature sensor. If you fix the chassis to the shower head pipe it'd probably be accurate enough. Also, assuming you need to wait for your shower to heat up, you'd have a pretty good idea when your shower was hot too - when it triggers your automation for the lights!

Just make sure the sensor polls often enough or can be made to report on a significant temperature difference in a timely fashion. Something like this might do it: https://sonoff.tech/products/sonoff-zigbee-temperature-and-humidity-sensor-snzb-02p

Also avoid WiFi for buttons, connection and addressing takes ages and sicks for an instant response needed for something like lighting changes