The tree is an adjoining neighbors backyard with large branches that come pretty close to my house (Though there is a sizable gap, if it comes down under the wrong wind direction…) and are actually touching another neighbors roof.
If it is unhealthy, is it recoverable? I’d rather not have them cut the whole thing down (it provides a lot of shade for my backyard (well, when it’s healthy that is lmao)) Should I talk with them directly (I don’t really know them, at all) or let the city know?
Hard to tell, but an ISA certified arborist will tell you straight. If in the states, you can look that up or contact your local state or university extension office for reputable certified arborists.