How do you screw stuff into the walls?

I am not worried about the screw pulling away. More about the screw pulling the laminated planet apart. 

Thanks. How much weight did you put on the connection?  I would like to install shelves. 

Re whether the foam does anything to help or not, it's normal in engineering practice when you have this kind is situation to just assume it makes no positive contribution to supporting the load. That is a conservative assumption but a good one.

Re pressure sensitive adhesive (PSA) tapes, they have been around for decades now. They can provide a strong bond if applied right and used in the right environment. If installed wrong or used under conditions they're not intended for they can fail badly. So if you use them follow the directions carefully.

Personally, I don't trust them, having had some bad experiences with them. Mechanical fasteners have to be installed correctly too of course, but they are much more tolerant of varying temperature, humidity, and surface prep. I have no objection to LA's "belt and suspenders" approach of using both.

Also don't be afraid to perform a test to see how strong your attachment is. It will have to hold up one way or another, might as well find out sooner rather than later.

If you test you need to put the right amount of force on the attachments in the right direction, which requires a bit of thought. For example, upper attachments of shelf brackets primarily see pullout loads (because the weight on the shelf is trying to rotate the bracket outwards st the top) while bottom attachments mainly see pull over loads. The pullout loads are worse because of leverage from the shelf, so it's going to be the upper shelf bracket attachment that fails first. So if it's a shelf bracket it's best to install the bracket and pull down halfway out the bracket (where the center of downforce on the shelf will be) rather than directly on the attachments. Use a spring scale and pull down with about twice the weight you plan to put on that bracket to account for bump loads while driving. Hold the force for awhile. If it passes that test you should be good to go unless you're using PSA tape which fails later due to environmental conditions.

I built a cabinet over the kitchen counter for dishes plus 2 towel bars and toilet paper holder in the bathroom.