I have the same system and issue in my 2017 mazda 6. It wants to recognize anything in the car except my phone, including a wireless speaker we brought on vaca once. It remembers my husband's phone, my old phone and the speaker that isn't in the car. If I fiddle with it long enough I can get it.
My phone is old and I think the Bluetooth connection isn't up to par.
I have an iPhone 13. Prior to getting this phone right after i bought the car, I had an iPhone 6S plus with which the car had no issues. Go figure. Either the sound system or the iPhone 13 is stupid.