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While I appreciate your additions to this thread, the Oxford English Dictionary would slightly disagree with you.
The Latin word was indeed gaudere, which morphed into Anglo French gaudir. The OED then says about gaud “perhaps an Anglo-Norman noun” from gaudir<gaudere." Note that the earliest meaning of gaud were “A trick, prank; often, a device to deceive, a piece of trickery, a pretence; also a game, sport, or pastime.”
The noun gaud shows up by 1386(Chaucer), but the adjective “gaudy” doesn’t appear until 1529, where it still means “trick.”