You said that magnetic field density (eg in Teslas) = energy (eg in Joules). that statement is false, end of story
Can a magnetic field do work (energy) on another object or field? Of course, the answer is yes. Grab a magnet, put it on a table, and put a steel ball bearing nearby. Does the magnet attract the ball bearing? If so, then it took energy (joules) to do that work.
Don't continue to dig this hole that you've already dug yourself into.