Please follow the instructions at the official repository.
We advise using the latest stable version of 3D Slicer with SlicerMorph, as updating SlicerMorph is much simpler that way. If you opt to use a preview release, remember that you will need to download and install a newer release to get the updates.
Currently, SlicerMorph is not searchable through the extension manager in either the preview build (4.13.0) or 4.10.1.
SlicerMorph is not available for 4.10 series. Try either the latest stable or the preview (I saw it should be available for todays build, as I downloaded earlier today).
I have both the 4.10.0 installation, and the preview build of 4.13.0. The 4.13.0 is not showing SlicerMorph or SlicerRadiomics as downloadable modules.
As I said, SlicerMorph is not available for 4.10 versions.
As for your issue with 4.13, occasionally extension builds fail for the specific preview version either due to a bug that crept in during an update or due to a problem with build system. You might have downloaded 4.13 version that suffers from such an issue. These are usually fixed in the next daily build or so. So, try with a newer preview build. I know that SlicerMorph is available at least for the 4.13 in the last 3-4 days…