The approach shown above would be doable -- selecting each worksheet would allow you to swap out the blue or the pink sheet, but you would build a resulting BLUE and a resulting PINK worksheet, and the action would determine which one is showing. You'll need a dimension to pass between the original worksheets and the resulting sheets as well.
There is no way to shade the background sheet "shading" property based on a condition currently, but you can certainly use the Marks card to color a "square" on the sheets -- each sheet would use the square mark type, and you'd end up with 4 sheets total. The two top sheets you currently have, and then a dynamically swapping third sheet based on user selection.
This is not a simple process, so if you are just starting out with Tableau I would recommend a simple parameter to allow the user to choose what set of worksheets they are viewing, as shown here (I would learn this process before trying to figure out the ones above, as well.... https://www.thedataschool.co.uk/hashu-shenkar/tableau-tip-switch-between-views-dynamically-on-a-dashboard/