Methaphysical theses are claims about what exists, what kind of things there are at the most fundamental level.
Don’t confuse with what Hegel/Marx/Engels/Lenin polemically call methaphysical, hammered into that literature here:
Link to originalWhat Engels calls "metaphysics" roughly translates to "un dialectic"
Maps to what we’d today call essentialism about “natural kinds”, the reification of analytic distinctions, and static/snapshot thinking as opposed to process thinking (can’t understand a glider (GoL) by looking at a snapshot).
His reasoning: classical metaphysics since Aristotle tended to analyze being through fixed essences and rigid categories, so he labeled that whole static/categorical habit of mind “metaphysical.”
physicalism
dualism
idealism
materialism
Metaphysical necessity
Metaphysical necessities are necessary in the sense that the world could not possibly have been otherwise.