I have been using Outlook for the longest time and have tried FairEmail a couple of times and simply deleted it. Tried sticking through it for about a month and I'll be sticking with it for a good long time now :)
You can add an outlook account to the gmail app. You may have to add it as Microsoft exchange instead of a regular Outlook account though, but the process is the same.
I suggest you use Outlook Lite instead of the normal Outlook. It's a lot lighter and will not prompt you to add any MDM profiles if your institution set any up