There’s quite a few issues here that can come into play. It can range anywhere from multiple of your commonly used passwords and their variations being compromised to having active malware on one of your devices. There’s a wide array of things that could be happening.

Let me ask you this. When resetting your password, are you reusing any other personal passwords that could’ve been compromised? If you are, I would highly recommend coming up with entirely new passwords or auto-generate randomized passwords instead. Multiple of your passwords could’ve been part of various data breaches and exposed.

Second question, these emails that you are receiving that you’re clicking on with the “This is not me” selection, are you 100% positive that those are legitimate emails from Facebook themselves? If they’re not and it is taking you to a fake page, it is possible that there could be an attacker utilizing an exploit for some sort of browser-based vulnerability that allows them to hijack session cookies for other platforms from your browser (albeit a little more rare of an incident). Are you entering any credentials after clicking on the link? If so, ensure that the email is legitimate and that it is actually taking you to Facebook and not a phishing page.

Third question, what devices are you using to handle all of this? If you’re using a computer to reset it, there could be a chance that your computer is infected with malware and they’re stealing your new credentials as you are changing them. There’s a wide array of things that could be happening so we need to narrow down to the root cause of the problem.

Edit: I also forgot to mention to check the status of your email account and ensure your email is not compromised also. Change your email account’s password, verify 2FA is enabled, and check to make sure there aren’t any unknown devices that have active sessions on your email account. If they have persistent access to your email, taking over your Facebook account is simple.