This is a very good edit.  Your attention to trail meta data is exemplar. 

The trail that was removed should not be added back but not because it is private property.  Instead, the trail should be removed because the original edit was not quality controlled by a person but instead an automated road atlas import (TIGER) from over ten years ago that is continuously being corrected.  

OSM follows the principal that only what exists is mapped and does not follow private property exemptions unless contracted and approved through data@openstreetmap.org.

I have some doubts on the house that is titled, "The Last Homely House East of the Sea" as a de facto broadly recognized name so I would consider if this is true and whether it should be removed.  I googled it and only found a youtube channel of a british cottagecore infulencer.

[https://www.youtube.com/@thelasthomelyhouse]

Overall an excellent edit to an under mapped area.  If you have a curiosity to do more, I would be interested in seeing more detail in the Elka mine area. 

Congrats. 