No this would be used in places where you would use SQLite or rocksdb
Are there databases for embedded applications, such as ARM microcontrollers?
Probably SQLite if not just flat files
Putting SQLite onto a controller that isn't running a full OS is actually a lot of work. [0] There isn't a working RTOS port out there, last I checked.
I've used ports of BerkleyDB several times for things down at that level. It isn't very powerful, but it's enough you can use it for most microcontroller needs.