I spent a lot of time in libraries growing up, as a college student and as a young military wife who never had enough money for books. I spent even more time in libraries while homeless, as detailed in this Reddit post.
While homeless, I looked for parks and libraries with outdoor spaces where I could eat a meal and ideally wash up afterwards in a bathroom. The best libraries were also near a grocery store with a hot food deli and one or more other eateries and not too far from a park.
If you want your library to be as useful to homeless patrons as possible, try to make sure it has outdoor areas where it's okay to eat, trash cans in or near those areas and nearby food options.
If it doesn't, try to add them.
Yes, it's possible to add or attract eating options. Some libraries have little kiosks on site that sell coffee and the like or have vending machines. It's harder but not impossible to try to encourage a grocery store or fast food place to open close by.
If you hose down the tables regularly to keep it clean, try to do it at the end of the day, not the beginning. That way the tables and benches have time to dry overnight and people aren't sitting in water to have breakfast nor setting up food and drink in a puddle.
If homeless patrons are tying up pets outside and it's a problem, try to brainstorm a better option than simply having animal control remove them.
Maybe you can set up a covered outdoor area with electrical outlets and wifi access that allows pets. That way homeless people can at least charge their phone and get online, which may be two of the biggest reasons they go to the library.
It's totally reasonable to insist the animals remain on a leash and so forth, but please don't make it outright impossible for homeless people to have a dog and also go to the library.
Most homeless people are on the street alone. Their dog may be a beloved pet they refused to abandon when the world abandoned them. It may may be a much needed service animal, even if it lacks official certification as such. It may be essential protection in a dangerous situation.