I learned quite a bit in the past few days. So separate Share To extension will allow to accept text/URL from another app. In addition, custom URL Type will allow MyApp to be opened from another app (tested with Safari).
Now so far, so good. I keep reading that Share To extension is not allowed to open its host app (MyApp) directly with openURL method. If this is true (and it appears to be), then what other way is there to force the Share To extension to open MyApp?