Need Recommendation for Wi-Fi capable Receiver for Pool Speakers

A lot to unpack here. I assume the 3 speakers are still there? If so, unless they are wired in a strange way, I wouldn't run 3 speakers. I would only run two, optimally the two that are the furthers apart unless one is ridiculously far away from the pool area. That way you are using a two channel amp and things are much less complicated.

If it were me, I would be worried about strange impendences messing up my new receiver. So you'll need test the speakers back at where they terminate. You'll need a multi meter for this. It's a little involved, but worth it. (All of this assumes the wires aren't labeled) First, disconnect all of the speakers from the speaker wire. Then twist the two ends of one of the speaker wires together. Go back to the speaker wire termination location and test for continuity. Find the two speakers you want to use and reconnect them. Google how to test speaker impedance and follow the directions using your multi meter. Make sure that the readings are roughly the same and that range is within what your amplifier can handle. At that point you have the speakers sorted out.

For step two, Find a receiver that has Spotify connect and you should be good to go in that regard. You could also use the outputs from a dedicated Alexa device (or similar) to control music the same way.

Sonos amp supports 4 speakers. Just do that and call it a day.