your headline is good except the term "serverless".
please drop it.
The term means much more than "not hosting it on a server". As somebody pointed out, "embedded datastore" may be a better term.
I agree the term is confusing now that "serverless" has a cloud-related definition, but in the database world, it is traditionally one of the terms used as an antonym to "client/server database". See, for example: https://sqlite.org/serverless.html