Basically, the moment I sign in, I am signed off. Or at least, so it appears at first; any and all urls I go to, including the url I redirect to on login, will take me back to regular , under which I apparently am not logged in. However, if I manually try to use https by typing in, or type in the whole `https://secure.byond..`, byond recognizes that I am logged in again. Once I click basically anything, however, which will be linked as regular "*", it does not recognize me yet again and asks me to login.

I think this actually started affecting me a year or two ago, but I didn't really login much so I figured I'd come back to it later. I am experiencing this both in Windows 10 and Ubuntu 18.04, on both Chrome and Firefox, and it has happened now with two different accounts. I'm not using Https-Anywhere or anything like that, all browsers mentioned are completely vanilla (although for the hell of it, I just tried Https-Everywhere anyways to see if it would at least keep me on https, since that's where things work, and it did not). I am currently posting this by editing the html of the 'add post' page locally to send this form through Anyways, thanks for any help you can offer!

I have gotten Https-Everywhere to work, I am now able to stay logged on through that
I'd like to try to diagnose this with you if you can page me or talk to me on the BYOND Discord.

HTTPS Everywhere isn't actually a solution to your issue because it's incompatible with the site. Various things including forum posts typically won't work correctly.
Oh sure, I sent a friend request through the name Zdo10 on discord as you appear to have DMs disabled, although I am realizing now you might have literally meant speaking through that server itself, which is also fine.
Ping me on the server and I can send you a friend request from there. Might take us a while but I'd like to get to the bottom of this.