What, exactly, is matte?

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FWIW, in English the traditional theatrical term for 2D panels & backdrops is "scenery flats," or just "flats" for short, so named because they are flat. There are both theatrical & "Hollywood" types, differing in a few construction details, the latter type more durable & used in film & TV work. In theatrical work, flats are sometimes used to block the audience's view into the wings of a stage, a form of masking, & for that use are often painted a dull, flat black or dark grey color so they don't reflect light & distract from the look of the scene.

So "flat" as in color or dimension; as a type of background, backdrop, or mask; & the various uses of "matte" are all loosely related terms. English does not care how much confusion things like this cause. As James Nicoll put it, "on occasion, English has pursued other languages down alleyways to beat them unconscious and rifle their pockets for new vocabulary."