Do I have to register my business in other states if I do Amazon FBA?

I’ve been looking into creating a small business and selling on Amazon via FBA for a few months now, doing research and all that. I’ve seen a lot of tutorials on YouTube mostly covering dropshipping and how to list products, but I’ve never seen someone cover almost any of the business-legal aspects of actually running a business in the US on Amazon.

Does every business who uses FBA actually register with the state that their inventory was shipped to? Let’s say you live and operate your small business in Texas and your inventory is sent to California and Virginia. In Texas you would have to file a franchise tax form since that is your home state. And since you have inventory in other states it technically means your business has a nexus there and your business is required to register there.

I’ve never seen anyone online discuss this so I’m not sure if everyone actually does this or not. Anyone have any guidance on this?