Ah, I seem to have fixed both issues - it had to do with Control Room in the audio connections menu not being set up correctly, according to this page. Under “Monitor 1” it was not connected. I pointed it to my interface’s primary stereo out and now it all works - real-time render in place + export as well as the media browser previews.
However, it did warn me that it had to break the connection I had previously established to my interface on the “Output” panel. So now Stereo Output is disconnected:
I am not sure if this is an issue, though, because playback of my timeline is working ok. I guess I haven’t understood the difference between this Output page and Control Room, so when I originally installed Cubase I set up my interface on this output page instead. At least I got it working!