Installed the firefox app on current version of firefox with windows os. When i click the app in firefox it shows "sign in via google & sign in via facebook" If i click either one it signs me in and opens a new tab for the websites home page. Now if i click the app the two sign in buttons are still there instead of the anime on my currently watching list from MAL. My Mal account is connected and properly shows everything on https://notify.moe/animelist/watching. What is the issue that is causing the app button when clicked to only display the two log on options? No matter which one i use it will only log me in and open the new tab. Is there a solution to change the app once clicked to display show titles like seen here: https://lh3.googleusercontent.com/2oIRuRDpO9QWv3yQjI6F-5vHEs0EXMBhUsTM4MKx4pMQF5u4Dy_g2uSyKQo0GjRXWf3tA7EBtHk=w640-h400-e365
Firefox app not working as intended
There are no "MAL connections", there is only a one-time account import. This is an independent tracker.
Your issue seems to be that the cookies from your normal tabs don't apply to the extension. You say you are logged in via normal browser windows but not logged in via the extension. That is indeed very weird and I can't reproduce your problem locally. When I log out, I'm logged out in both. When I log in, I'm logged in in both.
You can try to disable bad ad blockers like Adblock Plus and try uBlock Origin instead.
Another problem that might be occuring is that your cache is very outdated. Try clearing your cache to make sure the extension is not accessing any old data.
I would also try reproducing the same problem in Chrome. See if it works in Chrome for you or not.