This is two releases back (we’ve had 2025.12.0 and now 2025.13.0). Version 2025.13.0, released yesterday, addresses both of your concerns (see the “NEW” section of the release notes).
They’re performing a staged rollout, so you might not have the most recent release available yet. But check in the Play Store to see if there are any updates available to install (I had to do it manually). You can also join the beta from the app’s listing in the Play Store so that you can have access to new releases sooner.
To get rid of the Discover, On Demand, and Live TV content you’ll need to disable it in your online media source settings:
https://app.plex.tv/desktop/#!/settings/online-media-sources
Set Movies & Shows, Live TV, and Discover Source to “Disabled” (not Disabled for Managed Users). That will get rid of the On Demand and Discover tabs in the nav bar and remove their content from the home screen. You need to force close and reopen the app for this to take effect. It will also remove Live TV content from your home screen. Once you’re on 2025.13.0 or later it will remove the nav bar button as well.
Finally, once you’re on 2025.13.0 there’s a new setting to configure the default page for the library view. It can be configured to be the Browse tab.