If you're a mega hit TV show like The Bear, one of the few problems you'll have is that suddenly your actors are pushed to stardom, meaning they're going to pursue other jobs as well as your stellar series.
To avoid that, the creators behind The Bear wanted to shoot both the currently airing Season 3 and Season 4 back-to-back. However, even though this was the plan early on, it seems that didn't end up happening.
According to The Playlist, eventually the script writers simply couldn't come up with the scripts fast enough, and so while a little bit of Season 4 filming was done, don't expect a super-quick turnaround from Season 3.