While there are technically no known limits to the amount of groups one can add in the Assignments Tab, if an excessive amount of groups (more than 30-40) are added, the wait time to load the page gets excessively long in the web app (but not the phone app). I have around 80 groups or so, and it takes about an hour to load some of my Assignments Tabs for certain courses. I absolutely *need* to have a lot of groups. I homeschool, and I use the Modules as "Subjects," and the Assignment groups as "Days" (Day 1, Day 2, Day 3, etc). Without this, things can descend into chaos really fast. I've already contacted Canvas, and the workaround is simply to use less groups.
I am hoping with enough votes, Canvas would consider re-coding their Assignments Tab to support more groups. I use the Android app sometimes, and the Assignments tab loads relatively quickly, even with a lot of groups. So it's definitely possible.
Currently, I have to start loading the Assignments page for 3 different courses, early on in the day, so that later on in the day it's ready for me to start working on. I then publish the next day's work (rather than "finding" all the next days work by clicking through each module), add 2 more groups for 2 more days so that I go to the modules tab and start adding the different assignments under the subjects (modules) for two of those new days I added. Then, every Friday, I use the Assignments tab to go to 5 groups (days coming up) and schedule the due dates for the next week (opening each assignment under a group in a new tab to add the due dates).