Airplay does not allow me to connect to both Apple TV HD and the HomePod Mini simultaneously.
It doesn’t have to. You can connect the HomePod Mini to the Apple TV in Control Center. Just AirPlay (video+audio) to Apple TV. Then Apple TV will direct the audio to the configured speaker.
Moreover, not all Web-based streaming sites have the Airplay option.
If you can’t use the in-app AirPlay option in Safari, then you can usually screen mirror the Mac through AirPlay. Not as good/smooth (screen capture re-encoding), but often effective enough.
Apple needs to address this problem. Why hasn’t it thus far?
It works as intended. The ‘Why’ questions are a bit fruitless, as the reasons for corporate decisions are not communicated beyond the exceptions of what is desirable marketing-wise from their point of view.