It depends on the application of course, but some of them do end up sprouting a bunch of little "quality of life" JS functions. Writing these is happily a much simpler experience than it was in 2012! The most complex app I run also has the deepest browser support requirements, back to IE11. That said, I still have document.querySelector in all my target browsers so I find I don't even need jQuery.
For autocompletion, datepickers, etc I use drop-in components. These tend to be jQuery based but it's not the end of the world.
When I do have a particular view or flow that outgrows the "bits and pieces of JS" phase it's actually pretty straightforward to use a modern UI library like React or Elm on that view alone. Reducing the scope of the area you're using the framework in rather than writing the entire app in it simplifies things pretty dramatically. The JS doesn't need to worry about routing, pushState, etc etc etc. It just deals with its own little patch of DOM and state.
For autocompletion, datepickers, etc I use drop-in components. These tend to be jQuery based but it's not the end of the world.
When I do have a particular view or flow that outgrows the "bits and pieces of JS" phase it's actually pretty straightforward to use a modern UI library like React or Elm on that view alone. Reducing the scope of the area you're using the framework in rather than writing the entire app in it simplifies things pretty dramatically. The JS doesn't need to worry about routing, pushState, etc etc etc. It just deals with its own little patch of DOM and state.