When you save your footprint to a new library, you are asked for the destination etc, which you should have done by looking at your post, when you create a new footprint if anything has changed (or if KiCAD thinks anything has changed) then it will say "changes will be lost" blah blah, this is quite common.
Now, as you have noticed in your "current library" list it isn't there! This is a common annoyance in KiCAD, but it does allow you finer control - even if you don't want it! You have to add it to the footprint / library list.
Within the footprint editor, go to Preferences -> Footprint Library Manager.
You will see 2 tabs, one for "global" and one for "project specific", the difference is simply, the global tab will allow you to use your library on all projects, project specific is for your existing project only.
Once you have determined which option you want, you click the "Append with wizard" button, it will then bring up a dialog box asking if you want to look on your local machine or a GIT repository, follow the screens from there.
Once complete, it should appear in your "set active library" list, and you can then work with your new library from there.
HTH