[I’m OP, just under a different account.]

I forgot to mention a small detail: the *bʰāt- root for “boy” seems to be an old reconstruction. Usually Proto-Indo-European roots have three consonants, and even short *a is surprisingly rare - and it’s mostly from borrowings, like the Semiticism *táwros. There’s a Proto-Slavic root that might be related, too.

Another possibility is baby talk, given the original meaning associated with “father”. That would explain the weird vowel and structure.

One of those reposts where I’m just glad to see it again because it’s so good lol.