Does InDesign have a similar 'Type object selection by path only’ as Illustrator?

Those two tiny textframes that you illustrated might easily be produced as one textframe, and therefore the selecting would become easier. I am always looking for ways to let the paragraph style do the layout work for me.

https://www.rorohiko.com/wordpress/indesign-downloads/likefindslike/

No, there is no similarity there like you have in Illustrator preferences.

But you might consider organizing textframes on a text layer, and graphic object frames on a graphics layer. If you lock an upper layer, you can freely select things on the lower layer.

Another idea is to Cmd/Ctrl+click down and past and through the top object to get to the object you want underneath. This is an operational keyboard-and-mouse shortcut (and it works nicer than the same trick in Illustrator).