Is telling my mom's longtime friends her diagnosis violating her HIPAA rights?

No. That law was made for health care personnel. You send them all a note perhaps saying she's having some medical challenges... Here's her address if you wish to send her a card or note.

This doesn't make sense to me. If a family member has cancer, or a cold, or a broken leg, we routinely inform family and friends of the family member's condition without regard to HIPAA. Why would Dementia make it any different?

HIPPA does not apply to a layman in a non-business environment. You will be fine.

No. It is only for professional caregivers. You can share what you want. You would not believe some photos that family post on social media. Medical staff would frequently remind family if they thought their loved one would want them to share.

If you are the one responsible mainly for your mom's care and well being, and you know her relationship with these friends, there's nothing wrong with reaching out to her friends to inform them of her condition. Especially if your intentions are to try to encourage her friends to spend some time with her. If it were my mom, I'd consider the benefits of telling her friends and the possibility of them coming to see her and it would outweigh my concern about HIPPA. The biggest question is does your mom have a lawyer on standby waiting for you to mess up so he can file a law suit? If not, tell her friends and try to bring her some joy by encouraging them to come visit her. Best of luck, and no matter what, spend as much time with her yourself as possible because that is MOST important!

HIPPA rights ONLY apply in a medical setting. If you think it would be helpful to let her friends know so they can interact with her via "snail mail" and bring a bit of joy to your mom, then so be it.
It will hurt no one and could bring mom much joy and make her feel less lonely.

And I wouldn't give up on trying to get your mom to go to an Adult Daycare Center, as most folks that go there love it.
Most places allow you to bring folks on a trial basis. She won't know if she likes it if she never gives it a try. They do such a great job with those that attend. You couldn't ask for better.

"The Privacy Rule applies to all forms of individuals' protected health information, whether electronic, written, or oral. The Security Rule is a Federal law that requires security for health information in electronic form."

HIPAA only applies to covered entities and their business associates.

It does not pertain to private individuals that I can find.

source: https://www.hhs.gov/hipaa/for-individuals/guidance-materials-for-consumers/index.html

Your Mom is not going to sue you nor is anyone else. BUT and HOWEVER, her friends are almost certainly aware she is different at this point, and almost certainly aware that--for whatEVER reason--she is no longer capable of being their friend. They will survive that. They are already long distance friends. So, no, I would not reach out to her friends. If they reached out to me I would tell them "I don't know if you are actually able to reach Mom or if you have spoken to her. If you have you may be aware of some difference in her. She is facing some of the aging issues that will come to us all if we live long enough, and I think she is not at this time capable of maintaining long distance relationships. Why don't you just send her some pretty cards; I know she would probably love seeing them." I wouldn't do more. These are, as I said, long distance friends at this point. There is no reason to overshare.

I agree with all of the above, but if you are mom's POA that binds you to keeping any of mom's information private. Anything you do must be as mom would do.

We even see frequent posts here from siblings that are not updated on health information by POA sibling.

I don't know that you have to share the exact diagnosis. You might just let them know she is having a hard time, unable to get out much, would love to hear from them. At our age, we are aware that cognitive issues and depression are often at play.