Thank you @Mayer M. I appreciate the reply and I’m grateful for the information. Still have a ways to go! Any suggestions on PO Box or virtual address?
Out of state LLCs must register with the SoS as foreign entity if they "do business" in Texas. Don't worry, there's a definition on the website. Technically, buying or selling real property is not "doing business", neither is leasing or letting property.
However, foreign LLCs cannot bring a suit without registering. And eviction is a lawsuit. You can defend a suit, but won't be able to bring your own claims in that case.
Even if you don't register, you don't have to have an address in Texas. You can keep your NY box. As a last resort, TX SoS will be your address in TX. That office will forward to your NY SoS to deliver to the address you have on file in that state.
Adjust your business model accordingly.