FastMail is an email service offering paid email accounts. It also allows to manage calendars and contacts and provides CalDAV/CardDAV interfaces.
In order to use 3rd-party applications like DAVx⁵ or Thunderbird with FastMail, you need to generate an app password. Choose "Mail, calendars and contacts" access.
Choose "Login with email address" and enter your FastMail email address and the generated app password (see above).
Hint: When using fastmail with your own domain without SRV records you can try to use the Login with Base URL method and use
https://carddav.fastmail.com as Base URL together with your Email address and app specific password.
Contact group method: groups are separate VCards
You can mount your fastmail files using the DAVx⁵ WebDAV mounts feature.
User name: your fastmail email address or username
Password: your password