The... impromptu harmonizing wasn't like, 100% totally unplanned, pick a random person and just go for it, right on the spot, literally 0 prep.

I have no formal vocal training or precise understanding of the relevant terminology though, so I may be misunderstanding here, but anyway:

What I would do is just listen to a number of other people sing, if someone had an actual, even kind of stable range, and ability to at least come close to demonstrating intentional pitch control..

Then I would go up to them, say hey, your voice, your singing is actually quite good, would you want to try a duet?

If yes, then we'd try to plan a song, and go to a quiter part of the venue or just outside to do at least a little bit of harmonizing practice, pick our vocal roles in the song, then go and try to do the actual song.

... I guess that is ... more impromptu than like, regular structured training with a choir or band mates or something like that?

As to the Rock Band thing:

It sounds like you got further into, or had more experience with the game than I did, but yeah, for me also, at least one of the Rock Band games, maybe the original?, was the first step toward me realizing... oh, there's like, actual defineable patterns in music and vocals, and this is at least one kind of way of representing them!

And then from there I kinda just did my own investigation and self teaching/training, learned how to play an actual bass, would just sing songs I liked to myself, to see if I could match them...

A lot of the Beatles' songs are imo a good set of songs to try to replicate, because you have such a wide variety of levels of intensity, and complexity, range... buts its more or less the same main vocalist, the same baseline.

Start with maybe Blackbird or When I'm 64 ... then try to do Paperback Writer, but also have yourself do all the backup vocals along with the main vocals, in time, or try to really nail Yesterday... and then move on to Back in the USSR, While My Guitar Gently Weeps, more intense or wide ranging songs.

Also, this is maybe neither here nor there, but I once had a... kind of long distance relationship with a gal who... she hated her own voice, but just loved mine.

She'd have me just literally read chapters of a book to her, till she fell asleep... over skype or discord or whatever it was... from literally the other side of the planet.

Said I could be a voice actor or professional narrator, audiobook recorder.

But, that was before machine language synthesis had reached the point it is now at so... yay for that...