On my current home, fresh water comes in from the street on the uphill side
of the property, and the sewer goes out toward the street on the downhill
side of the property. There are two sewer cleanouts - one less than 2 feet
from the edge of the house and one about 35-40 feet away, close to the
sidewalk that runs along the street.

The cleanout closest to the house is simply a length of 4" CPVC (I guess?)
pipe dropped down a snug hole and loosely resting on the actual sewer pipe.
The sewer pipe is notched where the cleanout meets it.

Is it normal that there isn't a physical connection where the cleanout
meets the sewer pipe? I expected that to be sealed T connection.

Many years ago when I lived in Omaha I had a situation where a tree had put
its roots into the sewer pipe, plugging it up and requiring excavation. We
don't have trees here next to the cleanout, certainly not that close to the
house, but it still seems less than ideal.