Well, my experience with avocado is limited to growing them in containers, but I have been growing them for over a decade (I think?) so I guess I have some opinions
Looking at your avo, I'm jealous because it takes mine twice as long to reach the multi-branched, multi-growing points branch tips that yours has in ... 4 years? My avos spend 7 months indoors because it gets too cold outside, so I'm guessing it's the difference in the length of growing season and of course the tiny containers they are forced to live in.
Pruning -- WELL -- I HAVE to prune to get them to fit in the house. I understand though, that avocado wants a certain number of growing points/branches to believe it is mature enough to bloom/fruit. I follow the basics -- keep the branches growing outward, cut off inward growing branches and cut above a bud growing out. Avoid crossing branches. Rather than cutting, you will be better off training the taller branches downward by bending them -- tie them down or hang weights. I've been doing that by tying the branches down to nearby, fences, even down to the handle of the bucket they are in.
You could cut the central leader if you want to keep the tree from getting too tall and easier to manage/care for, but ordinarily, avocado's are big trees. Watched a YouTube video of how they were keeping avocados short for ease of harvesting at a commercial orchard, though.
As for why your tree hasn't leafed out. I have a couple of guesses and questions, one possibly a bad thing.
So, when the big branch fell, did the avocado lose protection from blazing sun? Was it exposed to more sun than it was used to and get sunburned? -- Black patches? Crispy leaves?
Are you fertilizing your tree regularly? I keep hearing avocados are heavy feeders. They sell fertilizers formulated for "Citrus and Avocado" -- I have to special order them, but I assume they are generally available where you are.
Along the same line of thought -- those big palm? trees behind the fence -- could they be stealing nutrients from your avo? What about the tree that dropped the big branch?
My avos have started leafing out already -- usually they have a growth spurt right around Spring Equinox. Three of them that are flowering bloomed starting around mid-Feb, and others that aren't yet started budding out with new leaves. Of course mine might be following a completely different schedule due to their indoor lifestyle. It's *almost* time to send them outside for their short growing season.
OK... the bad thing. (Hopefully not the case) are those white powdery patches on the trunk? I had a purchased "Day" avocado grafted onto Haas. It became listless and weak, and then started to lose entire branches. I couldn't understand why until patches of white starting creeping up its trunk. Where the white patches grew along a branch, the branch died. It's some kind of disease. I looked it up and was pretty sure, but I couldn't get confirmation. Before it spread to the entire tree and killed it, I took cuttings and grafted them onto some of my other seed-grown avos and two of them survived, so I was able to "save" it.