It’s really too early to tell because it depends a LOT on how various organizations implement Matter support.
What you’re looking for for what I think you want to happen. You want Alexa and/or Google and any other infrastructure you want to connect to to support a Matter Bridge. A Matter bridge would expose devices behind it as Matter native devices.
Then they also need to support the Matter Multi-admin features.
Unfortunately right now it doesn’t look like you’re getting Matter bridges from Amazon or Google for the near term. That’s up to them to implement. Amazon has already announced the ability to onboard certain Wi-Fi based matter devices on certain Alexa and Eero devices but they’re waiting on Thread.
HA would need to have a standards compliant implementation of a Matter Controller (which that’s a good bet its going to happen)
So very early term. Good time to pull out some popcorn and see what happens.