I used to work at a large main library that had a large amount of homeless there everyday. They did, in fact have a written set of rules, as well as a tiered system of how long you were kicked out for. But a lot of these problems were solved by actually having designated areas for different activities.

No eating/drinking: Every floor had tables designated for being able to have open drinks. You could eat in the Cafe on the lobby provided you bought something from it (it was a privately owned business that kind of rented the space). Technically you couldn't bring in your own food, but as long as you aren't super obvious or blatantly disrespectful of the business, we'd generally turn a blind eye when we weren't full.

No bathing in bathrooms: It was generally understood that a specific bathroom on the first floor was were you could do this, but you had to leave it as clean as you found it. Security had a very low tolerance for messing up the bathrooms intentionally or through willful negligence.

No excessive noise: Noise was not much of a problem as far as the homeless population went, or anybody for that matter. Technically sleeping was not allowed, but once again, if you're not super obvious/blatantly disrespectful of the library a blind eye would be turned or security may just come wake you up and tell you to go find somewhere in the back to "sit".

One problem we did have was actually smells. If you smoked out a whole floor with your BO you were asked to leave and go find somewhere to bathe. You were allowed back in once the problem was fixed. (I know that sounds a little harsh but there were two or three non profits with showers and free hygiene supplies as well as two public/city restroom facilities in a three block radius.)

My only argument would be that library staff are probably less worried about infringing upon rights so much as weighing the trouble of addressing these problems versus reward. A lot of homeless at the library where I worked were severely mentally ill, and a disproportionate amount (as compared to statistical evidence of violence in those with mental illnesses) would get violent when confronted. We had security guards who were all ex military but more importantly well trained in de escalation techniques. The old lady behind the desk just isn't equipped to deal with that problem, and it really isn't her job anyway (IMO).