I decided to test it out on a website[0] and it does seem that the useragent goes by the Firefox name:

Mozilla/5.0 (Windows NT 10.0; rv:102.0) Gecko/20100101 Firefox/102.0

On my Firefox:

Mozilla/5.0 (Macintosh; Intel Mac OS X 10.15; rv:109.0) Gecko/20100101 Firefox/110.0

It's interesting to note that the Mullvad browser seems to be based off on Firefox 102.0, which came way back on June 28, 2022:

https://www.mozilla.org/en-US/firefox/102.0/releasenotes/

[0]: https://gs.statcounter.com/detect