I thought .dng was "All-in-One"

The big picture is that, by default, the edit history is stored in the catalog. If you want to restore edits to files, simply open the catalog that contains the edits, and reconnect the images to the catalog.

The above is true regardless of the file format, but it can be changed using the setting the others described. Or, edits can be written out of the catalog to selected files if you choose Metadata > Save Metadata to File (in Library) or Photo > Save Metadata to File (in Develop).

The difference with DNG is that the metadata edits can be written into the file, not requiring an XMP sidecar file. Raw files need an XMP sidecar file because they’re read-only, but formats such as DNG, JPEG, and TIFF allow Lightroom Classic to write metadata directly into the file itself. It’s just that it doesn’t happen by default.

Because it doesn’t need to, really. If I was in your situation, I would use the Folders panel to relink the catalog containing the edits to the DNG files in their current location, and that should re-associate their edit histories with the files.

Auto Save or manually  (Command/Control) S. Or you can update via the menu for metadata and previews. 

Autosave really is the best option. 

For the edits to be embedded in DNG files, you have to check "Automatically write changes into XMP" in Edit > Catalog settings > Metadata.

When you enable this setting, it will only affect new files. To embed edits into already imported files, select them in Library, and go to Metadata > Save metadata to files. Or press Ctrl + S.