Good test! Yeah, this has to be server-based. There's no way they're putting (probably machine learning-based, probably very resource intensive) image processing software with that kind of ability on phones (unless I badly misunderstand the capabilities of modern smartphones; mine's not a top of the line model.)

This article has some interesting tidbits. Reading between the lines a bit:

- That data is not only passed to a Google-controlled server, but the images are probably stored, and at least the relevant queries are saved to your Google identity (Edit: and also shared to other Google apps, such as Maps, to facilitate selling you things);

- They are either considering or actually implementing sharing it with other people;

- Google being Google, they may or may not tell anyone before they do that.