The reality despite what you or i might do, is that 99% of people don’t carry around an ethernet or hardwire in when there is available wifi.
The library might be public, but it’s still a good idea to communicate your intent or obtain permission prior to using someone else’s network in away they might deem to be unexpected.
“Do you have ethernet or wired internet?” is actually a common library question and the response from whoever works the front desk will likely tell you everything you need to know.