Why apps not working in background when I remove them from Recent Apps?

There is no need to close apps when you’re done using them, it is best to let them remain “in the background”. When you force-close an app it is no longer “in the background”. Force-closing apps when you are done using them serves no purpose.. other than to waste system resources. Apps that are in the background are in a suspended state and are not actively using system resources, so there is no point in force closing them.

(Remove them from the recent apps menu),

Do you remove from the recent app in App Library? Why?

The designation of Suggestions, Recently added, Utilities, Entertainment, Socal and others is for quick search and organize the apps on your iPhone in App Library.

It is not the intention to remove apps from the App Library.

You can use App Library to search an app you are looking for and put it back to the Home Screen.

See this Apple article: Organize the Home Screen and App Library on your iPhone

Organize the Home Screen and App Library on your iPhone - Apple Support           

OK, see -> Switch apps on your iPhone, iPad, or iPod touch

Switch apps on your iPhone, iPad, or iPod touch - Apple Support (IN)

-> scroll to Use Background App Refresh.