Lawyer sent me a collections letter but doesn’t have a signed contract (Alabama)

So this lawyer sent me a collections notice saying I basically owed him $1000 for a surgery I had about 6 months ago on behalf of the anesthesiologist group PLUS his fees of $333.33 and payment would be needed within 7 days or they would take further action to secure the interests of their client.

I used my google-fu and all I can find is something called the FDCPA, which I’m not sure even applies here in Alabama, and it says that unless I signed a contract saying I would pay those fees, they aren’t legally allowed to collect those fees from the debtor. I do owe the $1000 and I have made arrangements to pay it, but since they don’t have a contract with my signature on it saying I have to pay those fees, what happens if I just stop paying after the initial $1000 is paid?

I have a copy of the contract that the lawyer’s office themselves emailed me; the first page is labeled as “policies acknowledgement” and does in fact have my signature on it. The second page however looks like a standard payment contract that looks like it was meant to be filled out but was left blank by mistake.

https://imgur.com/a/Rv262Z4

This is the contract with all identifiable information blanked out as well as signatures but on the first page you can still tell where signatures were.