What is HDR, anyway?

HDR is just a scene-referred image using absolute luminance.

Not in the more general sense! It can refer to what its acronym spells out directly: Bigger range between dimmest and brightest capabilities of a display, imaging technique etc.

No. HDR can encode high dynamic range because (typically) it uses floating point encoding.

From a technical point of view, HDR is just a set of standards and formats for encoding absolute-luminance scene-referred images and video, along with a set of standards for reproduction.

No. HDR video (and images) don't use floating point encoding. They generally use a higher bit depth (10 bits or more vs 8 bits) to reduce banding and different transfer characteristics (i.e. PQ or HLG vs sRGB or BT.709), in addition to different YCbCr matrices and mastering metadata.

And no, it's not necessarily absolute luminance. PQ is absolute, HLG is not.

Isn’t HLG using floating point(s)?

Also DCI-P3 should fit in here somewhere, as it seems to be the most standardized color space for HDR. I would share more insight, if I had it. I thought I understood color profiles well, but I have encountered some challenges when trying to display in one, edit in another, and print “correctly”. And every device seems to treat color profiles a little bit differently.