USB3 is USB3, usb-c is only a connector. If a device advertised being compatible with USB3 you'd expect all of USB3 to work and it always has in my experience. Alt modes and thunderbolt are something else which is usually advertised. If a laptop advertised thunderbolt and didn't have that, you'd be right to complain.
Yeah, but that’s a less clear argument to make than “everything Bluetooth should always be interoperable”. Since Bluetooth isn’t universally interoperable (e.g. depending on the supported Bluetooth profiles), it’s not a priori clear that “doesn’t work with PC audio” may not be a reasonable technical restriction. Of course we know it isn’t in this case, but it’s not as simple as “it says ‘Bluetooth’ so it should work”.