If you got Barret, did you deliberately do it for the Trophy/Achievement or by accident?

I've only ever gotten Aeris, it took a while to realize it could also be Tifa or Barret. So it can be Yuffie too?

I'm wondering if the Switch version is specifically set. Like at Corneo's mansion, all four playthroughs he has chosen Tifa and not Cloud or Aeris.

I got Tifa when I played. It's not like I care because I ship Cloud with someone who is not on the party and unfortunately can't be taken on a date.

And from the options, I'd rather always get Tifa. Perhaps get Yuffie one time because you need to be a bitch to the others to take her.

So sad you can't select your own party members a make them go on a date however and whenever you want...... rip my non-canon ships

You should have created a no option, but it's alright.

I can't remember who I've gotten, probably just Tifa and/or Aerith. What determines who goes?

Certain options and actions throughout the game decide who goes on a date with Cloud. The wiki explains it better than me.

For Tifa, you gotta choose the options that stay more at her side.

For Aerith, same as Tifa, but in Aerith's side obviously.

For Barret, you gotta be rude to the girls and even be rude with him, in a certain way (I think?).

For Yuffie, just be an asshole to everyone.

There’s this invisible point system to determines who can go on a date with cloud, A website called Jegged goes into detail about in their walkthrough of VII.

So, how does that work? The only moment I can think of is calling Aeris the slum drunk or something, which I did once and still I got Aeris (I'm assuming saying that to her would count against her). I think I remember getting a flower once and having a choice of giving it to Tifa or Marlene, but I haven't been able to get that flower again or even remember where it is.

You get the flower from Aerith, when you first meet her.

To understand more about the dating mechanics, there should be a wiki page about it. If there isn't, merely searching a location and scrolling down a bit should lead you to a place saying Dating Mechanics, as long as that is a location you pass before the Gold Saucer date.

For example: in Shinra's Building, after rescuing Aerth and Red, you have the option to choose who takes Aerith away from the battle. Choosing Tifa will decrease the chance of going with her, but choosing Barret will increase the chance of him going. This is better told in Shinra Building wiki

Small choices gets different results