Does Italian cypress grow there? YOu should show a picture that includes the planting space shown from a distance.

More photos. Thank you for the comments.

I know the feeling. Just here to say sorry :(

We went through this a few years ago and ended up hiring an landscape architect. What has worked for us was planting trees that are umbrella shaped - main single trunk that then branches like an umbrella at the top of the fence. This worked great. The trees don’t take up much space in our yard and screen the neighbors second floor. A lot of trees that grow super tall are wide at the base and taper at the top, not giving much cover. I find that asking at a local nursery - not HD- you can get good advice on what will do will in your yard. We are further north but planted California pepper trees.

Looks like in the one view with the umbrella present that a single tree of that shape (post immediately preceding this one) planted in the spot where there is a gap in planting allowing the wall to show would take care of the new house addition.

I feel your pain. I live near the ocean in a tract of smaller single family homes that are all one story. Our neighbor behind us built into their entire backyard and then added a huge second story with a balcony off their upstairs master bedroom that looks right down on our home and yard. Their purpose was to have a (very distant) ocean view, but they completely blocked our very nice mountain view and took away our privacy. The lack of privacy bothered me the most. We planted bamboo at the fence line and have been waiting for it to fill in. It is not perfect (or for everyone) but each year we get a little privacy back. We did our research first and built in a barrier to keep it from going everywhere. We also are proactive and maintain it to make sure it stays in its lane, because the barrier isn't perfect. I think grape vines or bougainvillea would also give you some privacy, be easier to maintain, and grow nicely in your area.

Someone already mentioned CA pepper, but I think Mesquites or Palo Verde grow even faster. Buy 24" boxes and they will have explosive growth in one year. Just don't overwater.

Here to offer moral support. We are in a similar situation in the Bay Area with self-absorbed neighbors who thought nothing of starting a 28-week balcony extension project in the middle of a pandemic where many are working from home. Now, they have a great balcony with nice views and we’ve lost all the privacy in our backyard and dining room.