I mentioned this because it’s one of the things i didn’t know when i went to school. One of many things about socialization i was unaware of, largely because my parents didn’t know these things themselves, or care about them. My wife was much more helpful with this with our kids. Even my oldest who clearly inherited the weirdo gene from me was able to learn how to do this. I have continued to discover more about this through life, so much of it is simple like smiling, pleasantly greeting people, when people ask “How are you?” you just say “Fine, thanks” no matter how you actually are. Ask some socially well adjusted people for info, I don’t think I’m a great source for this.
Father of 2 boys currently aged 4 and 9, here. My advice: don’t sweat it. We did nothing formal with our boys before school, and they’re both getting along just fine so far. Granted, we are lucky in that they appear to be neurotypical with no health concerns, so far. They both went to nursery/pre-school for 2 or 3 days a week from age 1, and I think that was a huge help with social skills. It also meant they did some learning (mostly through play), which set them up well. We didn’t do anything extra at home - we read (past and present) and sing to them nearly every day, play age-appropriate games, helped them to dress and clean themselves etc, but left things like reading and maths to the professionals.
Also, your daughter has nearly a year of continued learning to go between now and when she actually starts school. She will almost certainly develop hugely in that time. I wouldn’t hold her back until age 5 - I think in most cases that does far more harm than good.

This is how I was as a little kid. I can remember my mom telling me that she was a little worried that I wasn’t talking. I had an older sister (less than 1.5 yrs older) who was an enthusiastic talker. But one day I popped out an entire sentence (Mommy, Carla chase the kitty). Thinking about it much later I came to understand that my brain likes to have a bunch of detail before it can coalesce everything into a coherent whole. If your daughter’s brain works like mine does, this might be helpful to being a good support for her.
I do wonder if it was partly our fault for not understanding her when she was saying single words, so she gave up trying. With a sentence there is more info, so it’s easier to guess even if mangled. Even now it’s sometimes hard to understand individual words without context. But it might be what you’re saying.

When she was interviewing at colleges she was asked about her sudden change from all A’s. She explained that her dad told her it was OK to get a few B’s in exchange for a social life. The people interviewing her agreed and she got into her first pick university!
I like your philosophy on this, and I’m glad the university was understanding.