Going to throw Dockhand into the list “things you can try to make container management easier”: https://github.com/Finsys/dockhand

I use a quick time for toggling on and off private DNS, and it appears it can also change automatically based on the network:

https://f-droid.org/packages/com.rbn.qtsettings/

It does require Shizuku to be installed, too.

First couple uses and I can easily see this replacing my Firefox search widget on my home screen.

However, when I click the search widget on my home screen, The app launches, but doesn’t put focus on the search bar so I have to manually click it again.

I would recommend having the app launch and the focus immediately going to the search bar within the app when a person clicks on the search widget on their home screen. That way they don’t have to click it again and activate the keyboard to search.