Confusion in modelling of total loop inductance of a rectangular loop
Assuming the inductance is a wire ~0.2 to 1uH/m depending on l/r or length to radius ratio of the wire and not a discrete small coil L then the radiating coupling fields of M will cancel on each opposing side.
While orthogonal fields  don’t couple (or affect each other, then each side will have an M value thus 2M, and depending on gap or length if square then simplifies to 4M which can be a small ratio of L. Inductance.
The M is small as you can imagine compared to a transformer where the coil gaps are almost touching ( except for magnet wire insulation winding method and core mu ) so in XFMR’s M approaches 0.99 .
But for a wire square loop where the H field flux density are attenuated greatly on the othe side thus M coupling inductance is also a small value yet measurably different than 4x L for  length, l in a straight wire.
This L value changes as the length approaches a 1/4 wave or harmonic of this and is ignored in this formula.
But if the link doesn’t make sense to you, neither will this answer.
Saturn PCB tool has a tab for this inductance loop.