How can I find out if my mom has been declared incompetent (and done legally) when the POA's won't give out the information?

This is a very sad story indeed!

I think that you are going to need to revise your goal. Instead of trying to get POA, aim for getting visiting rights, even if it has to be a supervised visit. Start with the ombudsman. Don't ask him or her to get involved in the family feud, just ask for help in being able to visit your mother. When you do get to see her, don't talk about your siblings, don't talk about disturbing topics, just show her your love. Talk about memories from your childhood. Avoid having her be upset.

If mom is in a dementia unit it is highly likely that she is no longer competent to revoke the current POA and reassign it to you. The other option is guardianship. Since your siblings would fight you on that, what would most likely happen is the appointment of a third party to be the guardian.

Hard as it is to even think about this, I suggest you focus on just being able to see your mother on a regular basis. Give up the struggle to have control.

If there's no record I would assume the guardianship didn't happen..

How or what will you help Mom with if you regain POA?

The information can only be disclosed in court as part of a Guardianship hearing. No other way.

Would an attorney be able to find out this information regarding competency? I cannot go any further in trying to help my mom, unless I can find that answer. If I can regain POA, there is hope for helping her. I don't and I will never speak to the current crazy POAs. The County Clerk's Office has no records to speak of regarding incompetency/guardianship.

If there had been a Guardian hearing, you would have received a legal notice of the show cause hearing. I'll guess that did not happen.
If two MD's--psychiatric or neurologic--declared her incompetent, you would not know that under HIPAA privacy laws. Only the Medical POA would have access to that.
If you want to see mom, ask for supervised visitation. This protects you from delusional reports by your mother. Ask to see the Ombudsman.

Contact the Bar Association they may have an attorney that would do pro bono work. Most attorneys will do a free half hour consultation. See if you can get access to probate court records. If social workers were involved I would be surprised if anything done was illegal. It is not at all uncommon for POA to have the decision making power of determining suitable living situation.