Messages app not opening for specific account on Mac mini

I have two Macs, plus an iPhone and an iPad - all of which are signed into the same accounts so that I can receive emails and messages on all of them. But recently I noticed that my Mac mini (sequoia 15.2) is not receiving messages on a particular account. I checked on my laptop, to find the difference one thing I noticed is that when I open "Messages" under the the Window menu on my MacBook I see a breakdown of the app and accounts, but when I click "Messages" on the mini I get nothing. Zip. Zilch. No window at all. I just reinstalled the OS, and no difference. Any suggestions?

[Re-Titled by Moderator]