WP Version - Version 6.1.1.
Plugin Version - 0.7.3
PHP Version - 8.0
Browser - Brave version - Version 1.47.186 Chromium: 109.0.5414.119 (Official Build) (x86_64)
STEPS

1. Enabled and setup "Time Based One-Time Password (TOTP)"
   Tested to see if it works : It Works.

2. Checked the Enabled Checkbox for FIDO U2F Security Keys and updated profile
   It reloaded with " FIDO U2F Security Keys" unchecked.

3. Disabled "Time Based One-Time Password (TOTP)" and updated profile.

4. Checked the Enabled Checkbox for FIDO U2F Security Keys and updated profile
   It reloaded with " FIDO U2F Security Keys" unchecked.

Unable to enable " FIDO U2F Security Keys"

When I tried this on another cloned install of the above, I first tried FIDO that didn't work, then I tried TOTP, that didn't get enabled either, nothing was getting enabled.

I tried it on Mozilla Firefox (109.0 (64-bit)) and I was able to get it to work, I was using the Brave Browser when I was facing the above issues, it doesn't work on the Brave Browser.
Also when I try logging in on the Brave browser and use FIDO it doesn't work, it works on Mozilla Firefox (109.0 (64-bit))