Question about Sony Cyber-shot DSC RX100 VII

From the version of the RX 100 V or VA, you can film "indefinitely" in HD, depending on the battery (approx. 100 min). The earlier generations have a limit because of overheating. With 4K there is still a limit because of overheating, it depends very much on the ambient temperature.

Exactly, that is described in detail, I can't add much more and I think the price is right with these extraordinary advantages, moreover small and always with you, otherwise there is no Sony camera either...!

There are certainly cheaper ones. In principle, long videos on small cameras are probably not quite trivial anyway because of the heat development. Have a look at relevant sites like dpreview.com.
I bought the camera because of the AF for still photos. I'm out and about a lot with kids and dog, who are mostly running. The performance of the AF is absolutely incredible, the tracking works extremely well, the camera finds the subject again even if it disappeared behind another subject for a short time. The burst rate can be adjusted and is breathtaking.
The image quality is good, but it can't hold a candle to a full frame or APS-C camera, especially in low light. But the AF makes up for it. I also really like the zoom range of 24-200mm, I'm happy to forgo f1.8 at 24mm.
For videos, where the AF is not enormously required, the camera is probably just too expensive. But take a look at the RX100 Va or the Canon G7X or G5X series.