Affirmative, Codeberg is the “official” public Forgejo instance and the organization which contributes the most to Forgejo development.

How about both?

Regardless of configuration, you still need to access the instance from mastodon.mydomain.tld or lemmy.mydomain.tld, but you can configure the Mastodon to use @mastodonuser@mydomain.tld as its identifier by setting WEB_DOMAIN to mydomain.tld.

Mastodon documentation on the topic: https://docs.joinmastodon.org/admin/config/#web_domain