You won't get banned for using a 3rd-party client or client mod, unless you abuse the API in doing so (which you're not likely to do accidentally).
Anyway, the short answer is: yes.
I think all of the major client mods on PC have anti-tracking plugins. I use Vencord which comes with a "NoTrack" plugin by default (it disables Discord telemetry, metrics, and crash reporting). It also has a "ClearURLs" plugin that removes tracking elements from URLs. BetterDiscord also has similar plugins.
You can couple these with OpenAsar (it's compatible with all client mods - I use it alongside Vencord). Along with speeding up your Discord, it also comes with a "DoNotTrack" plugin that disables discord telemetry.
On Android, you can use Vendetta which, again, has a "NoTrack" Plugin you can add that disables discord telemetry and tracking.
What exactly would you gain privacy wise from a 3rd party client? All communication goes through their servers anyway. I believe even voice calls go through their server and aren't p2p.
I use Asahi Linux on M2 - Armcord works great for me! Also, I’m pretty sure it’s still fully compatible with amd64/x86_64, for others though you might have to modify source, not sure.
Edit: additionally, I don’t think anyone’s been banned from discord just for using a client, the app uses the discord api under-the-hood anyway, but I think those who make the clients are more at risk if they use them, since they’re more likely to be noticed (repeated testing/debugging and such)
I get that, but one of your requirement was privacy. As others have explained that is diametrically opposed to the core architecture of Discord, so if you want that requirement then that is your answer.