Welcome to the forum
What you are experiencing is very normal. Most piggies will never like being picked up no matter how long they are with you. None of my piggies have ever liked being picked up and one of them was 7 years old (he passed away a couple of weeks ago).
Don’t try to pick them up with bare hands directly from the cage - they will see that as threatening. Instead herd them into a carrier/box and pick them up from there. It’s less distressing for them that way.
Once held, what then happens is very piggy dependent - some enjoy a cuddle, some tolerate it, some hate it.
I have had a mix of all! Only one is mine has ever enjoyed a cuddle; one is very friendly when in the cage but doesn’t went to be held; one tolerated it for health checks; the other hated every moment.
For interaction I have only ever sat with them on the floor and they have come to me if they wanted to. Holding them was limited to weight and health checks.
What you have seen in petting farms is not the normal way things go. Those piggies have either had it happen so often they are used to it, or more likely they are terrified of constantly being grabbed and handed around dozens of people - they are too scared to do anything about it.
A petting farm where the piggies don’t want to be held - which is the normal course of things - wouldn’t gain much attraction.
Much like the videos you see online of piggies being cuddled - they are for show with incredibly tolerant piggies: nobody wants to watch videos of the reality of piggy keeping
