And then I stumbled on the answer thanks to a random forum post.

Perform the following procedure when the unit is on.

1. While pressing DIMMER on the main unit, press AUTO/DIRECT to display the current setting on the display. While this is being displayed, while pressing DIMMER on the main unit, repeatedly press AUTO/DIRECT to switch the setting.

2. To exit the settings, release your finger. After a few seconds, the display goes out and the switching is complete.

Once the setting was changed to "Enhanced" HDR worked! But why isn't it in the manual? A bit of searching for the text finds a file called manual/sup/upd/hdmi_4k_pio.pdf .

So I assume that this is a supplement meant to update the original manual - it is mentioned as new functionality introduced after a firmware update. But why isn't it in the main manual?

If you visit the VSX-933 product page you can download the manual, but there's no mention of a supplement or an update. The original manual was released in 2018, and the supplement in 2019.

I wonder what other features this amp is hiding that Pioneer simply haven't bothered to tell anyone about?