What is the policy in your state regarding dementia and being of sound mind?

IMO its...if the person is competent to make informed decisions. Dementias differ. Some in early stages can understand what a POA involves, others have no idea. If the person can't understand what they are signing then they can't assign someone to be POA.

Whether or not you can sign legally, unless there is a letter saying you are incapable of doing so by examining MD, will depend of the attorney's exam of you prior to signing. If you are making, say, a POA he will ask you specifically and privately if you fully understand. He may ask you questions to judge you current mentation. That is why I recommend attorneys. When my brother asked me to be his POA and the Trustee of Trust the attorney said, right in front of me "Are you sure you know and trust this woman, because once you sign this she can sell the gold out of your teeth". It made us laugh, but it was true. He then spoke with my brother in private letting him know A-H every single thing I could do, including changing beneficiaries on his CDs, selling his home, and etc.
A POA signed and witness by notary is only attesting that it is you, you present ID, and that is your signature. But an attorney can attest that you are mentally capable of understandind what you are signing. It is much less likely to be "questioned" by entities.
I would ask this question of an attorney in your area.

My experience in FL (where my LOs live) is that the attorney does a private interview with the senior to determine if they understand the consequences of what they are doing/creating and to make sure if they came with someone, that person is not pressuring/influencing them to do it. It has little if anything to do with memory, and they attorney didn't ask to see any medical diagnosis from a doctor.

Rules surrounding PoA vary by state. I've not heard about "being able answer 4 questions" about family members as a test for their cognitive competency.