wordpress constantly redirecting me to /wp-login.php?redirect-to=…&reauth=1

Hi,
I have no clue when this started happening, as it had been a while since I logged into my sites (yes, multiple) running wordpress, but when I did go to update a vulnerable plugin a week or so ago, I can’t. What happens is I will click on login, it will bring me to the login page, and once I put in my username and password, it will bring me right back to https://2mb.solutions/wp-login.php?redirect-to=https://2mb.solutions/wp-admin&reauth=1 (the URL is in hex, but I just didn’t feel like copying and pasting directly). Very occasionally, it will actually bring me to the dashboard, but if that happens the next link I click on the dashboard brings me to that redirect re-login page. I have no clue why this is going on — as I said, I hadn’t changed anything before this started happening — but it’s driving me insane. I’ve gone through all the steps — clearing cookies, clearing cache, trying on different browsers, disabling all plugins/themes — nothing works. The only thing I could possibly think of is that it’s something to do with cloudflare (I use that to protect my website), as occasionally it will say something like ‘You need to allow cookies to login…’ but I do have cookies allowed. It doesn’t always do this though.
Any idea why this could be happening?
Thanks,
-Michael.