Config override per group

I've been looking into the group ecosystem, to see if it would fit a project I'm working on, but I have a couple of questions.

The basic setup:
Basic D10 install (basic page and article node types).
require drupal/group
Enabled group and group node.
Created a group type
Allowed only node content "basic page".
Created a group in this type (group/1, title:Group A, path: /groupa)
Created a group in this type (group/2, title:Group B, path: /groupb)

I have a couple of questions about this:
* When visiting "/groupa" I see a page with "Admin" as a title and "Roles". How can I set a particular node to be the page of Group A, and is there some submodule or config that allows me to set the site name, logo, and email (system.settings override) depending on the current active group ? Basically I think it would be some sort of group_config module that would override config based on the current group?
* When clicking on a "Group A" in the admin group list, the url is "/group/1", I would expect all references to the group to be /groupa (the path I entered) ? Or do I need to setup a path alias for this ?