Do HDMI installation cables differ from "normal" HDMI cables?

Um, no? A Verlegekabel simply means that it comes without a plug. A CAT7 cable also doesn't have solid conductors when you pull it off the spool.
Everything else is, especially for laypeople, an absolute disaster. 0.25² solid? That breaks so quickly, you just have to cough by accident.

Sorry, but the CAT5/6/7 Verlegekabel I have installed so far always had "solid" copper wire (0.55mm-0.6mm) as "conductors." The standard plugs, patch panels, keystones don't work any differently with the insulation displacement system.

Everything else is, especially for the layman, an absolute disaster. 0.25² rigid? That breaks off so quickly, you just have to cough accidentally.

If it breaks off that quickly, then you have usually gone for the CCA cable. It's saving money in the wrong place.

Thanks already for your answers. Since I unfortunately couldn't find an AWG value for my pre-assembled cable, it now comes down to a self-experiment. I have ordered one meter of AWG24 to compare which is easier to handle. Since so far no one has said that one cable or the other has a massive advantage, I will just see which one is easier to work with... Thanks for your help.

Small update from my side. My 1m test piece has arrived in the meantime and I am pleased that the cable cross-section is significantly larger than that of the cut-off device cable. The new cable has a cross-section of AWG24 (0.2050mm2), unfortunately, I couldn't find a value for the old one. In the picture, you can clearly see the difference again. Both cables are held at the same distance.