I'll give you the most extreme solutions I can think of, and let you decide how much of each you want to enact.
First and foremost: use a secure and privacy friendly OS—Qubes on a burner pc or GrapheneOS on a burner phone—with secure and privacy-friendly networking—use DNS-over-HTTPS, or self-host as much of the infrastructure as you can, consider a VPN, keep the device on an isolated VLAN—use a secure/private web browser like LibreWolf.
General rules of online interaction apply for maintaining privacy within the servers: e.g. don't talk specifics about your location, your age, your physical appearance, your childhood, your employer, etc.
As with most modern apps, the web app is necessarily less intrusive than the installable binary. Use the web app when you can, and limit your usage to only when you can use the web app on a computer and network you own—privacy enforcing habits are more important than all the software stopgaps in the world.
If you absolutely must use a binary, consider breaking Discord's TOS and using a modified front-end: I know some people who use Aliucord for Android, and I just this moment learned about GoofCord for desktop
don't install/run any software without verifying the integrity of the developers/distributors and binaries yourself, or building from source and verifying the code
It's better to have Discord stealing your browsing data to sell you shit than have some random github malware rootkitting your phone.