You might or might not be aware of some of this; if so, please ignore this. But here are a couple of things which could possibly make your experience with the new app more tolerable.
You can get all of that stuff out of the interface (except for the Live TV button in the nav bar). Visit this page and set (at least) Live TV, Movies & Shows, and Discover Source to “Disabled” (not “Disabled for Managed Users” but actually disabled). That will remove all content from those sources from the body of the home screen and also remove the Discover and On Demand buttons from the nav bar.
https://app.plex.tv/desktop/#!/settings/online-media-sources
You can get to the library list in two presses, the same as in the old app. You long press the Library button in the nav bar and a list of your “favorite” libraries is shown. If you further would like to see all libraries, there’s a button for that.
Something I’ve done to make it a little quicker to get to certain libraries’ content more quickly is to create smart collections for them. I then publish those collections to the home screen. It’s then a single tap from the home screen to view the entire library.
Having said all that, the app still has some stability issues to work out. But that will come.