SUMMARY
Upon managing to use the SDR ICC built-in profile first, then setting HDR mode, the HDR calibrator was correctly configured for my display's peak brightness. Unfortunately, it also defaulted the SDR brightness to equivalent to this figure.

STEPS TO REPRODUCE
1. Attach an HDR display. (in this case, Asus XG27UCS.)
2. Set display to HDR.
3. Set display to SDR again.
4. Set ICC profile to built-in.
5. Apply.
6. Enable HDR again.
7. Enter the HDR calibrator.

OBSERVED RESULT
HDR peak brightness is now the monitor's factory calibrated level of 486 nits. However, so is the SDR brightness level.

EXPECTED RESULT
SDR brightness should default to something comfortably below the peak brightness, such as 203 if supported.

SOFTWARE/OS VERSIONS
Linux/KDE Plasma: Arch Linux
KDE Plasma Version: 6.4.3
KDE Frameworks Version: 6.16.0
Qt Version: 6.9.1

ADDITIONAL INFORMATION
This is related to the previous issue I filed, #507439, which is how I arrived at setting the calibration level. This exact issue is why I had totally blown out colors instead of a perfectly adequate sRGB range for most apps.