Self hosted Wireguard is what I also use (though with WG Tunnel app rather than the official client for auto connect when I leave my home WiFi) but both support split tunneling when you edit the tunnel properties. Just check the AA app, save, and you’re good to go.

Which VPN provider are you using? Maybe look for split VPN in the settings or app exclusion. Then select AA and the warning goes away and AA also works as expected.