No white line on holes 2-9 waiting on the tee there doesn't seem to cause a problem...

I used to work as a Starter there(alone, without a partner for about 4 months), and I frequently had linked groups. I asked who the coordinator was, and once their first tee time was up, I asked him/her to "line them up". Although I didn't necessarily let them all stack up on the first tee, as long as they didn't block access, I let them ENJOY THEMSELVES?! I also allowed him/her to switch around whomever, as long as it was within their tee time(s). The only time I engaged them, was when they all stacked up and parked on the 9th hole, waiting for their groups to finish. I politely asked them to move away from the green(for both grass damage and safety), which they complied without complaint. OP, you need to call Evans Prairie and speak with the Pro. He needs to hear this. Before, during, and after my employment(no longer working TV Golf & Tennis), I experienced many different personalities, and wondered why/how some people were allowed to work there?!

But, etiquette says you're supposed to wait when you leave the green, between the green and the next Tee, until the group in front of you tees off...

You're not supposed to drive up to the next tee box and "cheer people on"...

(or in plain speak, "socialize"...)

exactly! When we play our championship course days, we usually have 3 or 4 foursomes. While we would never drive up to the next tee if there were strangers waiting to tee off, we often do it if the players on the next tee are from our larger contingent. We visit for a moment, razz a bit, and kill a little time while the hold-up works itself out.
No harm done. It's a pleasant exchange totally appropriate among friends.

I doubt many, if any, ambassadors would care one whit about it. Some rules are meant to be a bit flexible.

Just had this experience today, where the foursome behind us left the line after starter tried to hold them up, and drove to the tee box before we hit.

Didn't know them, they stood outside their carts in a yelling conversation about where to go for lunch. First two Hit through the noise, 3 asked them to stop talking. Didnt stop, I waited staring at them. One finally looked up and yelled you need to hit.

Smiling I said soon as You shut the h*** up I will. Lack of golf etiquette or just 4 jerks, u decide

Both!

Your experience is exactly why the line is there, and the rule exists for the next group to stay behind it. That would have been an appropriate time for the starter to come down and politely explain to the transgressors that they must move back to the other side of the line.

It happens, happens here, happens most places at one time or another. Happens at "nice" hotels and happens at "nice" restaurants. There will always be a certain number of people who (have one type or another of personality/self-esteem issue) HAVE to feel important and actually lack the skills needed to be "in charge" and yet not have to demand compliance. In it's most simple form, it's called theory "X", theory "Y" management. Had a starter once demand I get into the cart of a man smoking a very large cigar. I declined very very politely, and replied I would just take my own cart. He said, NO WAY, 2 carts for every FOUR PEOPLE, PERIOD. I said, no, smoke really bothered me too much, he pointed out GOLF is played OUTSIDE... so insulting. He came out the back door of the small starter shack, walked around the side to FACE ME, reached into his pocket, took out a cigarette, lighted it, and then after taking a deep drag of it, blow the smoke right into my face saying, "make up your mind, do you want to play or not?". I said, no, very meekly, never protested or got angry or raised my voice in any way. I told him it was fine, I'd just go home. I did go directly to the golf office which was on Wedgwood at the time I believe. I did have to wait to talk to any other than the secretary receptionist at the desk, but I waited it out, and finally was able to calmly relate, unemotionally, exactly how I had been treated with NO aggression on my part at all ! I was told the individual (I had first name and was from state of Virginia according to his pin) would be contacted for "further training". I told them my honest opinion was the individual would never have done this to a male... he probably feared that kind of bullying to another male could end in actual physical altercation ! The guy with the cigar got a HUGE kick out of it all, he and the starter "seemed" to know each other, or, perhaps they had some other link, I'll never know. When the Covid came along, I had to laugh to myself thinking how there were NO EXCEPTIONS to the four people two cart rule for ANY reason.... walked that one back fast didn't they... LOL ! Yep, the world if FULL of theory "X" mangers (meaning, their view is, people are by nature going to take advantage and manipulate, so you have to CLAMP DOWN ON THEM IMMEDIATELY, never listen or consider the circumstances !

I think you are indeed correct in your assumption that he wouldn't have done that to a guy, or at least, not to a guy who he felt could have kicked is ass.
When you had your conversation with the golf office, did you get any further information as to whether the starter was even correct about not letting multiple carts out? Even pre-Covid, I was told it was OK, and allowed to ride alone, making 3 carts in a 4-some, as long as only 2 carts were ever in a fairway at one time. It wasn't my idea. I was a 4th filling a group of 3 guys who knew each other and nobody wanted to ride with me. I wasn't smoking a cigar, either. Heck, I'd even bathed that week, so I don't know what the issue was.