How will this affect my taxes?

This will not affect your tax return  but you should be very wary of this agreement  and seek local legal advice before jumping into a situation you don't understand. 

Letting the company use your address would not have any tax implications, but being an "owner" might have tax implications, depending on how the new company is organized. And there might be other implications besides taxes, such as liability. You need to clarify exactly what your involvement is, and you definitely need a lawyer before you agree to anything.

This is a triple concurrence in that you need to seek legal and tax counsel.

Something about this doesn't sit right for me, albeit, we don't have many facts.

While states have been scrambling for $$ for years, COVID and remote workers have exasperated the impact.  

Some things to follow-up on:

• Are you an independent contractor? 
• Are you an employee?
• Depending on the response to bullets 1 and 2, tax consequences will vary.
  • Will you now be filing in two states?
  • Are you remote "for the convenience of the employer"?  This can be a hot issue depending on the states involved and the response to bullet 2.
  • What exactly are your responsibilities as a remote worker?

There are too many questions to really provide an adequate response to your question.  This is best addressed in a one on one meeting with the professionals mentioned above and in other posts.

The positive in this, is that you are asking the question ahead of time and not 6 months to a year after you have become a remote worker.  Kudos to you for being proactive.