The Outlook web app?
Seriously, saying you’re going to use Exchange without Outlook is like saying you want to play baseball but you’d rather use a tennis racket than a bat. Yeah, you might hit the ball, but that’s not the right tool for the job. With a third-party email client, you will probably lose calendar, contacts, and tasks syncing for Exchange, as well as 2FA, and the list goes on.
I actually don’t hate Outlook + Exchange Online from 365, and I am a Linux +GSuite user at home.
If we’re talking hosted Exchange or shudder on-prem, drop that ASAP.
Why don’t you want Outlook? Licensing?