Thank you for your patience. Please find our answer below. It’s a short summary after longer investigation and conversations with the team.

Tab Islands / Tab groups
We decided TI, in its current shape, doesn't fit AIR’s vision and is not aligned with UI. Therefore, it remains disabled to avoid unexpected experiences. We plan to adjust it in future and enable it in AIR, but currently it’s not our priority.
While doing the investigation for you, we were also searching for a solid workaround within the code but didn’t find anything of enough quality.

Extensions from chrome: store
Opera is not Chrome and vice versa. They're specific features that are not available in other browsers. There is a reason for it, and it impacts many things. That’s we have a dedicated store for extensions, which is maintained by a dedicated team. It’s still possible to install many of the chrome extensions outside the store, but we can’t guarantee their functionality.

Vertical tabs
This is an old topic among Opera users, but the answer remains the same. There are currently no plans of supporting such functionality in any Opera.
The vertical tab extension you mentioned from Addons.opera.com is something made by an external user. It’s not our implementation, but was reviewed and accepted by us.

Many thanks for all the in-depth questions, you seem to be a truly engaged Opera user. (edited)