Sorry, l forgot to include the photos.

Is the neighbor willing to plant another tree with less invasive roots & a greater distance from your fence? With you paying for the tree of course. 😊 Realistically, because of your narrow planting beds I think that’s the only way to regain privacy using plants. You might be able to plant a narrow evergreen in the 5’ wide section by the gate but looks like the neighbor’s tree already covers most of that direction. You don’t want plants that shed leaf debris too close to your pool. I’d think about adding an aerial arbor type structure all along that side of fence. You could either plant vines under it to grow up the support timbers or, make the top decorative enough that it could be a stand alone structure. Then plant true bedding plants that will do fine in your narrow planting beds. Here’s 2 structures in my back yard to illustrate what I’m describing as aerial structures. The longest one is to left in pic, the other is just above the red forklift & since summer it’s mostly covered by the bright green tree. It only has 2 sections compared to the 3 sections on the longer one. These structures let light & air through but provide a visual privacy break to the large property behind us.