Lightning strikes can induce significant current flows within all conducting parts of a building. This is obviously worse with parts that are not (or not well) grounded.

Basically without a lightning protection system you could stand next to a power outlet and a spark could bridge over to you and flow into the ground (there are slomo videos of such things happening in specific tests that have been conducted).

I think the shower warning app is a bit overkill. If your place is that frequently hit by lightning strikes I'd install a proper lightning protection system with a narrow mesh width and surge protection devices in all sections of the house. Yeah and ground that shower.

The hardest part about retrofitting such a system is getting a decent/low impedance ground connection. Ideally you'd embedded a steel mesh into the fundament and connect it to the lightning protection system on all sides. This is kinda hard if a house is already there, so digging deep on the sides of the house and trying to get connections under it (if possible) is the next alternative.

In any case make sure that ground impedance is actually measured..