This query is bordering on off matter, however to handle the Apple related query….

Which JRE does Catalina require? Or does one simply set up JDK?’

Catalina doesn’t require a JRE. macOS has no want for a Java Runtime Surroundings out of the field. You’d set up a JRE/JDK based mostly on your wants/necessities.

Now, because you talked about LibreOffice, a fast take a look at their System Necessities for macOS tells you what you want:

As a consequence of a problem, there are the next restrictions with Java: on macOS 10.10 and newer, JRE is not discovered, JDK is required

^{Emphasis mine}

You want the JDK.

OpenJDK is the Open Supply implementation of Oracle’s Java Platform, Customary Version. It’s the identical factor because the absolutely licensed Java Platform. So, in brief, it really works with all Java apps together with LibreOffice.