When you add a user into a new group, you need to log out, then log in again.
Or, if you do not want for some reason to re-login yet, you can use newgrp incus-admin. This command will launch a new shell with the new group enabled.
The reason why your non-root account needs to be a member of the incus-admin group, is because the Unix socket to connect to the Incus server, requires that incus-admin group membership.
In the following, the socket is not accessible by Others (---), and accessible by group incus-admin with permissions rw-.
When interacting with Incus over the Unix socket, members of the incus-admin group will have full access to the Incus API. Those who are only members of the incus group will instead be restricted to a single project tied to their user.
If you get permission errors with some commands, you may have to switch to the incus-admin group. You can verify with incus project list on whether there are restrictions or not.