I think that there's a tendency to think a technology is "a toy" if it is in a sense too good or elegant.
In the case of databases, I can well imagine Oracle or even Postgres people thinking that SQLite must be a toy because otherwise all the faff they do to set up and admin (and pay obscene amounts for) the databases is actually pointless.
Stands to reason. It is something you want to play with, not a figurine to leave on the shelf to forget about like some of those other database solutions.
SQLite works great as the database engine for most low to medium traffic websites (which is to say, most websites). The amount of web traffic that SQLite can handle depends on how heavily the website uses its database. Generally speaking, any site that gets fewer than 100K hits/day should work fine with SQLite. The 100K hits/day figure is a conservative estimate, not a hard upper bound. SQLite has been demonstrated to work with 10 times that amount of traffic.
A toy that can serve the vast majority of DB use cases. I get it, you can't build a massive-scale project with SQLite, but that doesn't exactly make it a toy DB...
Likely the second most widely deployed software ever. https://www.sqlite.org/mostdeployed.html
The best tested piece of software that I know of. https://www.sqlite.org/testing.html
People call it a toy database. Some toy.