How can I create a morning routine with my HomePod that would read me today’s weather? I believe this capability exists in other smart speakers, and even in iPhone’s Siri (to an extent).

I have a “Good Morning” scene setup in HomeKit where it turns on a few lights and starts playback of a radio channel on the HomePod, when I say “Hey Siri, good morning!”.

I would like the HomePod to tell me today’s weather as well.  

How can I accomplish this?
You can surely do it with the Shortcuts app. It's available on iOS and every shortcut you create will be synchronised with your other Apple products on the same iCloud account.

It works well with HomeKit, the default weather app and the Apple Music radio stations. You can trigger a shortcut with Siri, and you should check out the user guide for more infos.