Among the many things the late, lamented Eudora email client spoiled me for was, when I checked my mail, opening all the mailboxes that had received mail in new windows. That way I could click through, looking at each mail window and closing it when I was done, and be sure I had seen all my new mail.
This is a javascript you can paste into the FiltaQuilla addon’s “Javascript Action” filter action which brings this behavior to Thunderbird.
Following are the explanatory README, the script code, and license, embedded from my repo on Github at https://github.com/kupietools/filtaquilla-open-mail-folder-on-receiving-mail.