While the EU has introduced a common framework, EPR schemes are still administered at a national level, so the specific requirements, thresholds and registration processes vary between countries. That's why there isn't a single set of rules that applies across the EU.
That doesn't necessarily mean you'll need to register in every EU country. Some countries have registration or de minimis thresholds, while others have different requirements, so whether you need to register depends on the rules in each destination country and your level of sales there. Many businesses also choose to work with an authorised representative or compliance provider who can help manage registrations and reporting across multiple countries.
Unfortunately, we aren't able to advise on exactly which countries you'll need to register in, as this depends on your individual circumstances and the legislation in each market. If you're planning to sell across multiple EU countries, we'd recommend speaking with an EPR compliance specialist, who can review your sales and advise where any obligations apply.
As for the UK, US and the rest of the world, the EU packaging EPR rules don't apply in the same way. The UK has its own packaging EPR scheme, while other countries have their own regulations where applicable. If you expand into additional markets, it's always worth checking the local requirements, but they aren't governed by the EU packaging EPR framework.