Here’s a simple fix, and I believe the issue lies with Facebook. You don’t need to turn off two-factor authentication; it’s advisable to keep it on:
1. (Optional) Clear your browser data: Type “brave://settings/clearBrowserData” in the address bar. Check all boxes under the “Basic” tab. Choose “All time” for the time range and click “Clear data”.
2. Log in to your Facebook account using the Brave browser.
3. Click your profile picture, go to “Settings & Privacy” then choose “Settings” Find “Security and Login” Ensure “Use two-factor authentication” is on. Make sure you have the device registered to receive OTP (One-Time Password). In “Authorized Logins” click “View" select all devices, and click “Remove” Log out of your Facebook account.
4. Log in again. Enter your credentials and two-factor authentication code. Log out.
5. Log in again. After logging in, close and reopen the Brave browser. Visit Facebook; you won’t be prompted for credentials.
That’s it! This method worked for me. Let me know if it works for you too.