There's probably a word I've been pronouncing wrong my whole life that I don't know about
Just based on how often I notice someone mispronounce a word without realizing it (or have done so myself and realized it later). Statistically I'm probably still doing it with some word.
Both Oxford English Dictionary and Merriam-Webster agree that "nitch" was the correct pronunciation in both British and American English until very recently. You already linked Merriam-Webster, so here's O.E.D:
N.E.D. (1907) gives only the pronunciation (nitʃ) /nɪtʃ/ and the pronunciation /niːʃ/ is apparently not recorded before this date. H. Michaelis & D. Jones Phonetic Dict. Eng. Lang. (1913), and all editions of D. Jones Eng. Pronouncing Dict. up to and including the fourteenth edition (1977) give /nɪtʃ/ as the typical pronunciation and /niːʃ/ as an alternative pronunciation. The fifteenth edition (1991) gives /niːʃ/ in British English and /nɪtʃ/ in U.S. English.
(N.E.D is the original name of the O.E.D. "/nɪtʃ/" is pronounced "nitch" and /niːʃ/ is pronounced "neesh".)
It varies by region at least in the US based on a few years of doing service desk work. Listening to YouTubers, it seems a bit all over the place as well.