The formal/informal second person thing is fascinating to me as a Portuguese speaker.
European Portuguese, like many (most?) Romance languages, has the informal/formal second person split. Brazilian Portuguese has dropped the informal second person (tu) and uses only the formal second person (você).
Now, because “thou” is archaic, it sounds overly stiff, and most English speakers assume it was the formal second person, but it was actually the informal form. So both Brazilian Portuguese and English underwent the same process and chose the same way.
Also, "você" is actually not originally a proper formal second person. Grammatically, "você" is a third person singular. It comes from "Vossa Mercê" (something like "Your Mercy" or "Your Grace"), shortened to "vossemeçê", to "você". The origin, and still today a common gramatical construction in Portuguese in any formal or semi-formal register, is to use a periphrase in the third person to increase politeness. I guess in English it also exists, but only on the most fully formal contexts ("Does that right honourable gentleman agree...").
In English particularly, people associate "thou" with the King James Bible and similar Christian texts ("Our Father, thou art in Heaven…") and might reasonably assume that if "thou" was used to address the literal God, it must have been the formal pronoun – but the familial, informal one was used exactly because of the "father" association! (OTOH there certainly are languages with a tu/vous distinction where children were expected to "vous" their own parents – not sure how much of a thing it is these days).
Another fun thing is that calling someone you don't know "thou" used to be an intentional insult ("you're not worthy of being called 'you'"), something that might be missed by a modern reader of Shakespeare or other EME texts.