Perhaps. A key difference though - history files can include the individual pages I requested from the same host. Right now I have like 50 entries for the various posts I read just from HackerNews, all as separate line items etc etc.
In the case of the phone, one simply sees recipient of call, duration etc, regardless of how much information was exchanged. The phone I'm calling is arguably analogous to the server I request a page from, in the metadata context.
I'd argue browser history is significantly richer in some regards due to this. It's not unheard of for user identifiers to appear in URL paths either - try visiting https://news.ycombinator.com/user?id=<HN user name>... In my Chrome, that's instantly in the history file with my username.
The language spoken by participants during a phone call is also easily classified as “metadata” and could be defended as non-identifiable info with a straight face. So are the number of speakers on the call, the topics of conversation, the intensity of emotions displayed, voice stress levels, and the presence of certain keywords, if you squint a little. The lack of a literal call transcript does not matter much in terms of privacy.
I don’t know anything about this system, but the fact that screen shots are not ultimately stored on the user’s PC doesn’t mean anything if the content has already been classified and indexed. It will be fished.