At a guess, Adguard is blocking access to the URL that the router uses to do connection checks. You should be able to see that in the Adguard dashboard.
It’s the ‘Blocked by Filters’ link, second graph on the top row, or second in the General Statistics window on the left, and blocked queries are shown in pink(ish). I don’t know what the URL would be specifically but I would check for *.eero.com or *.amazon.com URLs that are being blocked.