Note: groups.io will be down for maintenance this evening, starting at 11pm Pacific Time (6am Tuesday 8/3/2020 UTC), for up to two hours.
this may be an anomaly due to the way I'm testing but I thought I'd mention it anyway.
From my 'owner' account using the web UI I send a message to my testing subgroup. When I open the email received by my 'member' account in that group and click on the Your Subscription link in the footer, I get a new Browser tab (I'm using FF) showing the subscription options for my 'owner' account.
If I initially click on the Follow This Topic link in the footer, it detects that this relates to a different account and I get presented with a login screen for that. It's the initial click on Your Subscription where this account detection mechanism doesn't seem to work.