Hi,
Welcome to the community!
All Dash components are basically dictionaries, so you can in principle save them as JSON or “stringfied” json. Here is a slightly related post about this particular point, however nothing is saved in a database…
If you are interested in saving inputs and selections, I would also encourage you to take a look on persistent props, which saves some of the selections in the browser cache. It is a bit more limited but simpler, since you don’t have to deal with user authentication and DB I/O.
I hope you’ll find this helpful, even if it is not exactly what you are looking for.