It's not about the packaging really. It could be as simple as a bubble wrap envelope. The problem is having to register in every country and some of them levy fees that are insane for small artists. The EU was supposed to be a single entity with simple rules but in this case they want to make things as difficult as possible.
The article could be clearer yes but it's really an issue especially for small self employed artists selling by post in the EU. They're basically being killed off if they relied on shipping to other countries.
And the risks of non compliance are high fines. This was meant to punish AliExpress and their sellers for packaging waste but how are they going to fine Happy Goose Ltd in a basement in Shenzhen? They're not. Business in the EU however are going to be easy pickings. So the Chinese will just keep what they're doing and the EU independent artists are screwed with retarded bureaucracy.
For an Amazon it's a joke paying 200€ to register in a single country, but for an artist that may not even have single package to a certain country every year it's insane. And you can't even register when you have an order to send, you have to do it before.
It's deeply evil and totally meant to kill the little guy or girl.
There's some exceptions for small business but they're mainly bureaucratic, the hefty fees still apply.
Are we sure there isn't some single market principle that overrules the presumption that you'd have to register in every country? AFAIK generally you're allowed to operate in one country and sell things to other countries, under some principle of single market / customs union.