This is very anecdotal, & I of course can't speak for all productions, but way back in the mists of time [the 80's] I used to do session BVs on occasion. Usually rock rather than pure pop bands, when people wanted what they would at the time call "Queen blocks" - huge vertical cliffs of vocals, from as low to as high as anyone could reach. I had a 3 1/2 octave useful range without falsetto, so it was a good time to be a singer for me.
I never saw a dot written, ever.
You walk in, they play the track, twice if you're lucky. then as that's going, someone will be saying - 'Yeah, right about here we need a bit af doubling on the lyrics, then you get an ooooh, oooeeoooh, to bridge that to the next line. Wanna give it a go?'
…and then you're on. Make it up as you go. The Producer will pull you up if there are better ideas or changes of mind in the control room.
Once you've got the basic structure down, you'll get instructions such as, "Let's get another couple over that, then one under. When we get to the big stuff in the chorus we're gonna block it up all the way' This will involve stacking maybe 6 or 8 different parts, depending on the complexity, with 2, 3 or four tracks of each to keep it smooth.
in some cases you start with 'the obvious' lines, the notes that make up the chord & transition with the melody. Then often after that, you get some 'squeeze & thicken'. This is the tough one sometimes. You try to find every possible note in the extended chord that hasn't been used yet;) Adding 4ths, 6ths & 9ths etc to otherwise solid majors to create 'cornflour'… thickener.
People don't really notice these notes, they tend to be buried back in the mix. But they generate a smooth 'wall' of vocals, very useful in many genres to 'thicken & glue' the BVs into a solid block.
All of this comes through 'skill & judgement', casual conversation, ideas from the producer &/or artist & a lot of trial & error.
I can't link to anything I did back then, but this is a snippet of something along those lines I did maybe 15 years ago, which I own copyright on, as an example of this 'fill every hole/cornflour' approach. It's just two simple choruses, one with & one without instrumentation. The block isn't quite as wide as we would be doing back then, but it gives you an idea.