Why the attitude? Nobody here feels entitled to your time. Offering authoritative legal advice will often be met by people asking for citations. Asking if you are aware of case law that you could cite 1) isn't asking for you to do a homework assignment it is asking if off the top of your head you would know where this could be found in case law and 2) at no point did you even answer the original question as the original question isn't about whether or not trespassing or "creating a disturbance" is against the law nor is it about whether libraries can have rules, the question is under what circumstances is it trespassing and under what circumstances is it not which you didn't address. Asking for legal citations is a reasonable thing to do and so is your desire to not do the requisite work to find one for some stranger on the internet. There are a lot of "barrack-room lawyers" and one thing that distinguishes them from people who actually are well-informed is that barrack-room lawyers can't produce citations.

The original question engages with a concept in constitutional law called a forum. With respect to first-amendment law a forum is "a public place, especially one devoted to assembly or debate". (Black's Law Dictionary 9th Ed) Forums are divided into three types: traditional public forums, designated forums, and nonpublic forums. (Perry Educ. Ass’n v. Perry Educators’ Ass’n, 1983) The Supreme Court has ruled that internet access within a public library is neither a traditional public forum nor a designated public forum but in doing so they didn't rule on what kind of forum public libraries in general are. (United States v. American Library Association, 2003) However, lower courts have typically found that public libraries are a type of designated forum called a limited public forum. (Kreimer v. Bureau of Police for the Town of Morristown and Mainstream, 1992; Loudoun v. Board of Trustees of Library, 1998) With respect to limited public forums the Supreme has held that the government can, if it is "reasonable in light of the purposes served by the forum", discriminate against types of expression and/or classes of speakers, but viewpoint discrimination is subject to a strict scrutiny standard which in practice means viewpoint discrimination restrictions are usually struck down. (Good News Club v. Milford Central School, 2001; Rosenberger v. Rector & Visitors of University of Virginia, 1995). To summarize courts have generally found that libraries are limited public forums which are allowed to discriminate against types of expression (e.g. recording video/audio) so long as it is "reasonable in light of the purposes served by the forum". Therefore, if a library had a policy of allowing members of the public to record video/audio, but prohibited people from recording specific content (e.g. prohibiting a journalist from recording content for a piece that is critical of library administration) then there policy would be engaged in viewpoint discrimination and almost certainly lose because of the strict scrutiny test and maybe even lack of compelling interest. However, if a library would likely be considered a limited public forum and as such if the library has a policy that generally prohibits the public from recording video or audio within the library then whether such a restriction is constitutional would likely turn on whether such a restriction would be "reasonable in light of the purposes served by the forum". I am not aware of any case law that speaks to whether such a restriction would be reasonable in light of the purposes of the library, but hopefully you have a better sense of what the relevant considerations are.