You can still use traditional methods to manipulate images, too, so I don't think a "does not contain SynthID watermark" means you can trust that image more. In the other hand, encoding a lot of personal and other information in the watermark (136 bit is a lot) that can not be easily removed and most of the people are unaware of it seems really an 1984-like dystopia.

The same techniques used here can be applied in other domains for other purposes. That would not "defeat its only purpose". The danger is the normalization of watermarking for [ insert good reason here ] with regulation eventually making it mandatory once everyone is accustomed to it. Rinse and repeat to gradually boil the frog.

We live in a world where nearly all printers already watermark everything they print with their serial number. It wouldn't be at all surprising if the next modernized variant of that technology encoded personal and contextual data tied to the user.