With Azir, Ascendant, does he have to pay the equip cost when attaching a swapped unit's equipment (like Doran's Shield), or does it attach for free?

Ruling: Azir does not have to pay the equip cost. Attach by itself doesn't involve equip cost.

Nuances:

• Equip is functionally short for "[Cost]: Attach this gear to a unit you control"
• Attach is the result of Equip, but attaching does not equal equipping
• When a card says "attach" without mentioning equip, no cost is paid