require() is on-demand loading. Once a module has been loaded it won’t be reloaded if the require() call is run again. By putting it inside a function instead of your top level module code, you can delay its loading or potentially avoid it if you never actually invoke that function. However, require() is synchronous and loads the module from disk so best practice is to load any modules you need at application start before your application starts serving requests which then ensures that only asynchronous IO happens while your application is operational.
Node is single threaded so the memory footprint of loading a module is not per-connection, it’s per-process. Loading a module is a one-off to get it into memory.
Just stick with the convention here and require the modules you need at the top level scope of your app before you start processing requests. I think this is a case of, if you have to ask whether you need to write your code in an unusual way, you don’t need to write your code in an unusual way.