PPWR for non-EU manufacturers
If packaging is placed on the EU market under your name or trademark, Article 3(1)(13)(a) makes you a manufacturer, with the Annex VII technical file and the Annex VIII declaration as your responsibility — wherever you are established.
It does not make you a producer. That role belongs to whoever first makes the packaging available inside a Member State, so registration and extended producer responsibility usually fall to your EU importer. You may appoint an authorised representative under Article 17 by written mandate, and the mandate can cover holding documents and dealing with authorities — but drawing up the technical file and the Article 15(1) duties stay with you and cannot be delegated. And if your importer puts its own brand on the pack, Article 21 transfers the manufacturer's obligations to them, which is a commercial negotiation better had before an inspection than during one.