my game, 10+cha is absolutely correct
i have many settlements that havnt bothered with that are under cap, but both my "big' settlements are capped at 16 (my cha is 6)
whenever i leave my beacon on (all the time
i forget lol) it stays at 16 and if i want to send someone there it is greyed out and i cant select said settlements.
now if i want to send someone there i just don my cha gear an voila i can now send
also because i constantly forget to switch my beacons off, when i don cha gear quite often will get someone turn up at settlement
these days my sanctuary is at 20, which is max for me (10+6(cha)+4(cha gear)=20) i purposely left beacon on for 2 days now as test and not a single settler has turned up.
formula is definitely 10+cha, and cha = your current cha not raw cha
but people have more you say? yes they do because there is a lot of bugs in this game (and exploits) ofcourse and for some reason even for what should be hard wired rules players are experiencing different "game rules" to each other.
for example you know how you are storing stuff at your settlements, well some players cant because any container at their settlements is restocking like a normal container giving them new stuff if empty but worse overwriting any stuff they store with random container stuff
also curie, many players cant send her to any settlement she just disappears back to her vault (known bug) yet many players also works fine, like me she's exactly where i send her everytime.
so basically the formula is correct, as for many players this is true
for those players who have more, then you are bugged/glitched/whatever you want to say
i say this being the official guide says this formula and it is true for some so it makes logical sense for those that its not true for would therefor be glitched or whatever you want to call it.