I know of at least three databases written in Java:

HSQLDB:

https://en.m.wikipedia.org/wiki/HSQLDB

H2:

https://en.m.wikipedia.org/wiki/H2_(database)

PointBase:

https://en.m.wikipedia.org/wiki/PointBase

I have briefly used either one of the first two, I think it was HSQLDB, with Java, years ago.

PointBase was created by Bruce Scott, a co-founder of Oracle, and a few others, including an architect of Sybase. This was in the early days of Java.

All three still seem to exist, according to the links above.