I consider it to be cache first, "db" second, with true definition of db first being something that can execute SQL or SQL like statements (such as Cassandra's CQL). It's the same reason I don't call Cassandra a cache, although it can achieve the same result.
true definition of db first being something that
can execute SQL or SQL like statements
Additionally, a lot of "toy" databases like Access can execute SQL statements, so the ability to execute SQL statements isn't necessarily a great way to tell what's a "real" database.
In practical terms, I do agree with you -- if somebody in 2023 is referring to "the database" in their app they had darn well better be talking about something robust and ACID-compliant like Postgres or whatever.