> This rabbit hole in the wikipedia has led me to a dead-end explanation
Trying to teach yourself physics by reading wikipedia is like trying to learn how to program by reading the C++ standard. It's a fine resource, but not for that. You need an introductory physics textbook, not an encyclopedia. Griffith's Introduction to Electrodynamics is a classic choice.
> those iron filings are pulled by virtual photons created by the magnet
No. Virtual particles are part of a notational scheme for carrying out certain computations in quantum field theory. They're not particles, and they're definitely not involved in classical electromagnetism.
> I've concluded that magnetism is an unexplained phenomenon, just like gravity: we have accurate formulas, but nobody knows what those formulas describe.
The formulas, ultimately, describe the relationship between our observations. This is the only sense in which we ever explain anything, and a sense in which magnetism and gravity are both very well-explained.
> For intuitive understanding, I see a magnet as a well, except that this well can be moved around and has two poles.
You should not try to understand electromagnetism intuitively yet. You haven't built the right intuitions, and to do that you first need to tear down your wrong ones.
Trying to teach yourself physics by reading wikipedia is like trying to learn how to program by reading the C++ standard. It's a fine resource, but not for that. You need an introductory physics textbook, not an encyclopedia. Griffith's Introduction to Electrodynamics is a classic choice.
> those iron filings are pulled by virtual photons created by the magnet
No. Virtual particles are part of a notational scheme for carrying out certain computations in quantum field theory. They're not particles, and they're definitely not involved in classical electromagnetism.
> I've concluded that magnetism is an unexplained phenomenon, just like gravity: we have accurate formulas, but nobody knows what those formulas describe.
The formulas, ultimately, describe the relationship between our observations. This is the only sense in which we ever explain anything, and a sense in which magnetism and gravity are both very well-explained.
> For intuitive understanding, I see a magnet as a well, except that this well can be moved around and has two poles.
You should not try to understand electromagnetism intuitively yet. You haven't built the right intuitions, and to do that you first need to tear down your wrong ones.