Pick the one you are held to
The standard is a setting, not a filter applied afterwards. Choose Level AA and Level AAA rules do not run, are not counted, and do not appear greyed out somewhere waiting to be noticed.
No inflated claims
WCAG 2.0 has no Level AAA in this tool because WCAG 2.0 Level AAA is not what the rule set covers. The regional standards run the exact WCAG set they adopt, and the settings page names it — rather than implying a separate, deeper audit that is not happening.
Start with the page you are on
Install the extension, press F12 and open the Accessibility tab. No account, nothing to configure, and nothing leaves your machine.