Does it? An 18th-century tavern owner could keep tabs on the comings and goings of their customers. It would have just prompted pushback when they started sharing that list.
Possession isn’t the problem. Sharing is.
The local or federal government do not have the right, or need to know the whereabouts of the average law abiding citizen. There is no "free" information, all information has a cost, whether it be acquisition or storage. Currently the people are taxed to oppress themselves. There is no choice not to be taxed, there is no consent.
The government, does not own the country, it's not "their bar".
Never mentioned the government. If I shop at a store and the store owner starts selling my information to everyone under the sun, I'm going to keep an eye out for alternatives. I don't mind them collating it. I do when they share it.
Which was trivially not covered by the 4th amendment [1].
[1]: https://en.wikipedia.org/wiki/Video_Privacy_Protection_Act
Also, "monopoly on violence" is deputised in a lot of ways, including "Stand Your Ground" laws, and "Castle doctrine" (which may or may not include a workplace), and what's allowed for trespass and if trespass includes not leaving when told to.
(And even when it's more of a first amendment issue than a fourth, there's also occasional news stories about people getting sued for leaving negative reviews of a business because the business snuck in a no-disparagement clause into the terms and conditions).
One does not violate the 4th and the other does (though they do it anyway).
The tavern owner is not the government. The bill of rights is about restricting the powers of the government, not of tavern owners.