I am afraid that you will likely get lost in the terminology unless you are very familiar with FamilySearch's use of the terms, Tree, New.FamilySearch.org and etc. I would refer you to my first post on this subject, if you need some help in this regard.
Assuming you now have all of the terms figured out, I will launch right into the subject of this post; preserving your files on FamilySearch.org's Trees.
Here is a screen shot of the FamilySearch.org startup page with an arrow pointing at the Trees link.
This menu item refers to a way to search the records formerly used in the old FamilySearch.org website, including the Ancestral File and the Pedigree Resource File. Essentially, although it is no longer mentioned as such, FamilySearch is inviting everyone to store their user generated family trees online and allow the files to be searched using this Trees link. Here is a screenshot of the sharing page:
You should note, that unlike sharing your family information on MyHeritage.com or Ancestry.com's Family Trees, you cannot view your file, yet, on FamilySearch.org. Clicking on the Submit Tree button shows the following page:
Once you sign in, you can see the following:
Interestingly, I could now delete the old incomplete backup file I up loaded in 2000. I could also store a copy of my current files online. You will notice that the upload is done with a GEDCOM file, which essentially means that some of the features of the newer database programs are not likely to be online for viewing or anything else.
This was always available as a contribution of your file to the Pedigree Resource File, but what is new is the ability to delete old files.