Stop attempting to override Accept header in [GitHub] API provider

[PyvesB]

Fixes #6960.

@chris48s, is this the kind of test you had in mind?

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[PyvesB]

The test failure will be fixed by #7012.

[chris48s]

Works for me. Tbh, I was thinking this would be more important in the case where we try to fix sending application/vnd.github.v3+json. It matters less if we just drop the Accept header but having a test for this will do us no harm :)