What type of outdoor speakers I can purchase to synchronize with HomePod Minis

Any active/powered AirPlay 2-compatible outdoor-rated speaker placed within solid WiFi range should work. I'm afraid I don't have any recent experience or opinions to share (just did a simple google search to see there's a variety to choose from).

One hint that will make them easier to enjoy is to add your chosen speakers to your HomeKit setup as accessories and create a Scene or two to get them playing along with what's on your HomePods and/or Apple TV.