Like-Kind replacement property...

"Does §1031 require that I only buy Like-Kind replacement property?"

The "Like-Kind rule" mainly applies to personal property, ie: "things you can move;" like supplies, transportation, machinery, equipment, inventory, etc. This means if you sell a pizza oven in an exchange, the new property must be another pizza oven.

But with real estate, ie: "things attached to the ground," you can buy any type of investment real estate to complete your exchange. If you sell a rental house, you could buy an office building, a commercial property, or even bare land. And of course you could always buy another rental house