Some browsers might accept both. My computer accepts both (although not the Gemini protocol, but it does have Gemini file format, and can read this over HTTP(S) and local files (including inside of ZIP archives, so gempub files can be displayed)). (Also, curl does not have Gemini (although I think that it should).)

There are some problems with using Accept header (although you can use it as a start; if you can implement it, then you might do so). Even if it is mentioned in the Accept header, servers will not necessarily understand it, and if a lot of file formats are implemented then it can make the Accept header very long, knowing properly the preference, trying to explicitly download the raw file or a specific other format (regardless of the Accept header), and other problems, etc.

(My idea is a Interpreter response header, although this requires that web browsers will implement it.)