I wear Birk EVAs - these are my beach shoes and they get wet and sandy and just wash off under a tap. Very comfy for walking too.

I wear waterproofed leather sneakers (unlined), or manmade fibre mesh sneakers (for all-day walking), or teva’s (universal sole).
I will often wear leather sneakers for walking to the office, then change into dressier shoes (because I like the dressy shoes but don’t want them to get soaked).

I know you live in a city, too: I steer away from open-toed shoes in a total downpour since feet get gross. I have a pair of Russel + Bromley patent loafers in a light color for precisely warm rain conditions and rarely wear them otherwise. If I don't need to by dressy, I usually wear these leather sneakers from Birkenstock which are indestructible. Or, if it's really hot and only threatening rain, I might wear platform Birks, which I see you have in your collection too.

Have a great time at the museum!

I wear fabric flats but not espadrilles. The jute bottoms do not hold up in water. Something that will dry well and not be sweaty wearing. I have some water or beach shoes that look like sneakers but are made to take beach walking and wet or damp conditions.