Can being a POA and bookeeper for someone be included toward the spend down with Medicare and Medicaid?

Yes, read the POA. If no provision for payment to the POA, then you can't take payment. Paying a bookkeeper is different. Just keep copies of the bookkeepers invoices to prove the expediture.

Any expenses that are for the principals benefit can be used to spend down to the Medicaid limit.
However a POA must be careful that they are eligible for payment. Read the document. If paying a bookkeeper for the principal out of principals funds that would be one thing but a POA must be careful of paying themselves as it could be construed as gifting and/or fraud.
A good use of the principals funds is to seek the help of a certified elder attorney licensed in the state that the principal resides in. Make sure the attorney is well versed in Medicaid procedures for that state. This would give the POA assurance that proper procedures are being followed.

There’s no Medicare spend down, it’s not based on financial eligibility. Just FYI.

For medicaid, there needs to be proper documentation and the income needs to be reported to the IRS otherwise Medicaid will consider it gifting and it will impact eligibility.

Are the funds being declared as income to IRS?