How to fix a leaking trim plate in shower
That is a Moen brand shower valve and trim. The escutcheon (trim plate) comes with a foam gasket surrounding the hole. When you push the trim plate over the stainless steel stop tube (cartridge cover), or when you push the stop tube through the escutcheon, the foam seals around it. The inside of the stop tube is leak free because it slides down over o-rings on the cartridge.

Italics indicate "official" part name.

You need a new escutcheon.

Can't comment on your "spigot" because we can't see it in your picture.

NOTE: this assembly is designed to resist incidental splashing. Prolonged exposure to high-pressure water douching will leak even with brand new parts. I have found them sealed up with caulking, which will work, but makes it a bitch to repair and therefore I charge more $$.