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Technically, you don't. The beauty of FOSS software is that you don't need to trust the author. I know that auditing the source code of something as large as a Linux Distro may be prohibitively difficult for one person to do alone. Groups of people do audit them though, and they have found nefarious things in the past, in the case of Google.

> I have to trust Mozilla to securely save my passwords and so on

You don't.

Pass, CLI tool from Wireguard's Donenfeld, Bitwarden gets good reviews, etc.

Why would you save passwords in a browser when there are FOSS utilities like keepass?