Now I wonder if I should really register a new account for each service. May I ask for your advice? What do you recommend?

Do you get any benefits from the accounts? You can subscribe to Lemmy communities from Piefed and vice versa. Piefed can now follow Mastodon users iirc. So do you get any benefits from having accounts on both Lemmy and Piefed separately? Are there other benefits to a Friendica account for you than following Mastodon accounts?

That's the important question really. If they don't have anything to offer to you that the others already provide, then you don't need that account.