Messages Delayed and Multiple Notifications in Teams Web Version

I communicate with teams from two separate organizations on teams, which requires me to be signed in to two different accounts at once. For that reason, I have to use Teams web version for one of them.

In that version, I've recently starting getting delayed responses. Then, once I do get the response, I get anywhere from 3 to 10 notifications that I received a message (both from teams, and from google chrome).

I guess first of all, is it possible yet to use 2 accounts at the same time in the teams installed on my PC? And if not, any idea how to fix this issue with the web version?