Note that officially the tested and supported Linux distribution for Oxygen v23.1
is Ubuntu 20.04.
The product has been fully tested on Ubuntu 20.04. The latest version of Oxygen might work on other flavors/versions of Linux, but they have not been officially tested.
However, from what we know Oxygen 23.1 should work fine on Ubuntu 20.10 as well.
java.lang.UnsatisfiedLinkError: /home/matthijs/Downloads/oxygen-64bit-openjdk.sh.815048.dir/jre/lib/libnio.so: /home/matthijs/Downloads/oxygen-64bit-openjdk.sh.815048.dir/jre/lib/libjava.so: version `SUNWprivate_1.1' not found (required by /usr/lib/rt/lib/amd64/libnet.so)
From the UnsatisfiedLinkError exception I would say the OpenJDK 15 Java runtime that is bundled with Oxygen 23.1 tries to load a native library from your system that is for a different version of Java. I'm guessing "/usr/lib/rt/lib/amd64/libnet.so" belongs to this OpenJDK 8 you have installed.
We've tried installing "openjdk-8-jre", but cannot reproduce the issue, the installer still works just as well. You may have something in your environment (e.g. a library path) that causes this.
Regarding the OpenJDK warning. While it's not mentioned there, Oxygen expects the JVM vendor of the OpenJDK JRE to be Oracle. However, for OpenJDK distributions from your Linux distro package system the JVM vendor is usually set to the Linux distribution vendor. So for Ubuntu the JVM vendor of the OpenJDK is Ubuntu, which isn't officially supported by Oxygen.
Anyway, this JVM warning can be ignored. But, since you're using OpenJDK from your distro, I would recommend using at least OpenJDK 11 since it's more recent and it's LTS.