I run an awful lot of MS email for a lot of customers. My own company (literally mine) uses Exchange on prem and I pass all access through HA Proxy. My customers mostly use M365 but one is still on GroupWise (I have known GroupWise for roughly 25 years)
I've seen browsers come and go. My first one was telnet on a VAX through a X.25 PAD and a string of connections via the US (I'm UK) to CERN. First graphical browser was Mosaic on Win 95. I think Mosaic became Internet Explorer - MS don't really innovate - they buy it.
Edge is basically Chromium with knobs on. Chromium is Chrome with knobs removed (sort of!) I can exclusively reveal that Firefox works fine with all version of OWA and Exchange on-line, because that is what I personally use and so do many of my staff and customers.
If you have snags with your uni email then there is something specific there and not your browser choice. Edge doesn't do anything special for OWA it's just yet another Google browser.