Perhaps try enabling HTTPS mode, if you have not already:
Edge is a browser. Microsoft’s only current browser.
Somewhat confusingly, it is based on the open source Chromium browser engine which was originally a Google invention. Google’s Chrome browser is very much the same app as Edge deep under the hood. Which is good news for website compatibility. But each of Edge & Chrome have lots of idiosyncrasies in how they deal with user-level preferences, features, and suchlike stuff versus how they draw a webpage on the screen.
What is the Google Store? On a Windows computer?
Yes, or it was called Google Play? I should have mentioned that part.
Which means you installed the Android version of the Discord app on a smartphone or tablet.
That is different from using a browser on a desktop OS like Windows.
Yeah, I’m a bit confused here. Was the issue on a Windows laptop or an Android phone? Or is there more than one device involved?
No, it’s a PC. Just the one device.
Do you mean you got it from the Windows store that I linked to? The Google Play store shouldn’t be involved at all, unless you somehow managed to install the Android version on your Windows PC (usually not doable without a lot of hoops). Sorry for the confusion here; not sure how we went from a Windows desktop app to the Play store… 
Anyway, but the desktop app is now on your PC, and that works 100% fine… but you can also log back in on a browser now and that mostly works now, except for a few missing icons? Am I understanding that right? Like you went from completely unable to access it through a browser to being able to access most of it?
That is even more bizarre. Does incognito work any differently now?
Are you even on a Windows PC…? Are you maybe using a Chromebook or something similar…?
Yup. I got on through the email verification the app sent. Of course, if I refresh that page, it kicks me out again. And yes, it’s a PC, not a Chromebook. Lemme try incognito again.
EDIT: Nope, incognito is still a no-go. 
An update that I suspect is connected to my other woes: I can’t download any documents from emails to my computer. Very weird.
And yet another update-I believe I figured out the culprit using Agatha Christie logic-what programs did I install around the time the errors started happening? Aha!
So what was it?
Something called TotalAV. It’s a virus-protection program but apparently, it was a little overzealous.
Thanks for the update.
More I wanted to boast about my own success! 