To disable the domain transfer lock, first deactivate the private registration

I’m looking to migrate from ionos to godaddy or similar. Referencing:

https://www.ionos.com/help/domains/set-up-and-manage-an-external-domain-at-11-ionos/removing-an-external-domain/

and, presumably, registering the domain with godaddy is simple enough. How do I ensure that everything is kept intact in terms of the domain registration?

I see:

Authorization Code

The transfer lock is enabled for this domain. For this reason, any transfer request will be declined automatically. The Private Registration is enabled for this domain. Before you can transfer the domain, you have to deactivate it.  

If you want to transfer your domain to another provider, you will require the authorisation code shown below. The authorisation code makes sure that only the Registrant or Administrator of the domain can initiate the transfer process to a new provider.

Please note that upon completion of a transfer to a new provider, all website content, email addresses and subdomains associated to the domain will be permanently deleted. Your authorization code:

However, wouldn’t want to disable an privacy around the domain registration.

Does this disable the privacy information available through whois or similar services?