MSI GE73. I have no audio interface, have only been using the onboard soundcard.

The onboard Chipset is one of the better ones. Cheap Interfaces like the Behringer UCA202 wouldn't produce better sound.

Regards
Tom

Alsa was being used for (non-Pianoteq) sound, it seems, but JACK was setup. Then I also plugged an amplifier plus surround speakers into the jack, but no sound from there either.

That said, I played with the studio-controls settings, and got it work. Like so often with Linux, I have no idea how I got it to work. I have not connected my keyboard to Ubuntu Studio, don't have time for that yet, but MIDI playback seems to work fine.

Pianoteq works on Ubuntu Studio, with the exception there is no sound through headphones.

What are the headphones plugged into? An external audio/MIDI interface? A sound-card headphone/stereo-out jack on the back panel of the computer?
Have you checked in Pianoteq and PulseAudio options to see which audio interface is being used (by default) and tried to change it to the one that the headphones are actually plugged into?

Are you using ALSA or JACK audio backend/infrastructure for Pianoteq and/or other apps that produce audio (like a web browser)?

In UbuntuStudio, check studio-controls-->System Tweaks and other tabs. You can open/configure/check PulseAudio devices/volumes by clicking the "Open Pulse Control" button in studio-controls-->System Tweaks.

Good luck.

I have a couple of questions, about installation and licenses.
Now as Pianoteq 8.0.2 is out, do I simply run the installation file to update to 8.0.2? It doesn't install version 8.0.2 on top of 8.0.(0, or 1) so there'll be two versions side by side? Do I have to uninstall the original version first?

No nee to uninstall, you can keep as many older versions as you please, as far as the installation is concerned. Just pick a different directory (obviously). Not sure about the license for doing that, but I think that's fine

No idea, I run PTQ exclusively on Linux (briefly tried PTQ on Windows and Mac in the past and did not like the OS a bit, so back I am as Linux-only)

Now as Pianoteq 8.0.2 is out, do I simply run the installation file to update to 8.0.2? It doesn't install version 8.0.2 on top of 8.0.(0, or 1) so there'll be two versions side by side? Do I have to uninstall the original version first?

Also, I'm contemplating installing Pianoteq on Ubuntu Studio 22.04, which is on the same machine as my Windows installation. It is dual-boot, though the Linux OS resides on a different SSD.

Will that count as an extra installation, even though it's on the same machine? That would mean I've used up all my three installation opportunities, already have Pianoteq on a second desktop computer.