Currently, there is no way to set the language of the developer tools GUI separately from the language of the rest of FF's interface. The developer tools should ideally allow a separate language setting, or at least a toggle to switch to English separately from the rest of the UI.
Why might a user want this? The main reason is that invariably the developer tools messages in English are easier to Google than a user's native language. As a byproduct, this means FF's errors/warnings messages in languages other than English may be unfamiliar to colleagues and require the user to tediously switch locale by going to preferences and then back again just to work on web dev with a colleague.
More generally, in many languages the English version of a technical term is better understood even by those who speak little English than its native-language counterpart. Thus as a matter of preference many folks may just find the English devtools more preferable even though the rest of the interface is more useful in their native language. Giving users the option allows users to use whatever works best for them.
A feature request for this in Bugzilla has languished for quite some time and it would be great to see more attention on this.
(Posted on behalf of u/Lenni009 on reddit—see https://www.reddit.com/r/firefox/comments/w0xd17/sunday_rantrage_20220717_your_weekly_complaint/igi0... One among many examples of users who would benefit from this setting)