I wonder if CSS could implement sqlite...
The database parts are dealing with areas that must have some triggering action (calling a stored procedure, running a trigger, selecting a resultset, that kind of thing) for anything to happen.
The lines are blurring, yes. What's interesting is the 4GL systems which do the reverse (colocate your apps with your data for speed).
I don't know if it's still the case or not, but Oracle had the option to run a web-server as part of the database at one time. Back in the Oracle 8 or Oracle 9 era, as best as I can remember.
EDIT:
OK, here we go.
https://docs.oracle.com/en/database/oracle/oracle-database/1...
You can use an embedded version of the PL/SQL gateway that runs in the XML DB HTTP Listener in the database. It provides the core features of mod_plsql in the database but does not require the Oracle HTTP Server. You configure the embedded PL/SQL gateway with the DBMS_EPG package in the PL/SQL Web Toolkit.
Some advantages of using the embedded gateway instead of mod_plsql are:
You can invoke PL/SQL web applications like Application Express without installing Oracle HTTP Server, thereby simplifying installation, configuration, and administration of PL/SQL based web applications.
You can set arbitrary headers with postgrest so you can use it to serve pages. I don't know if this is exactly what you mean but it's as close to "dbms with its own web server" as I've seen.
It's also just cool lol. Though as much as I like plpgsql and it would be hilarious to use it as a templating engine I don't really have a use for this.
E.g. I'm not aware of an, out of the box, elasticsearch interface that is not the HTTP API.