BTC recovery of registration details without a wallet.

Is there any way to recover my BTC from the registration process?

In general, there is no registration process to buy or extract bitcoins or for most types of bitcoin wallet. Certainly not in 2009.

I started mining in March 2009, I remember to register.

There is no registration process for mining. At least not in the Bitcoin software of January 2009 released by Satoshi Nakamoto.

At that time, I believe that mining would have placed any extracted currency in a direction controlled by the private key in a wallet on their PC, for which only you would have the password.

Registration for a custodian wallet service (exchange / exchange service)

There may have been a registration process if you had a "custody" wallet, a type of wallet in which you made arrangements with a third party for them to manage your wallet on your behalf. There are many of these companies, all different. In that case, you would have to contact the specific company with which you registered. This would not have been the case in March 2009, but perhaps in later years he has registered in a portfolio custody business to use his commercial services. (In any case, this paragraph may be useful for later searchers who find this question because they have the problem expressed in the title).

There are lists of inactive addresses, can they be used to recover my BTC?

No. To regain control of the BTC, you need the private key that was stored in the wallet. The address is not enough.