If there's nothing wrong with what is being said, then why should it matter who says it? Does propaganda somehow gain effectiveness because it comes "from the source"?

Sanctions are about impinging others freedom because they’re behaving badly.

“Why can’t I play with the kid who is in timeout? Is it because you hate my freedom?”

Except your analogy here should be more "there's a kid on timeout so nobody gets to play, just in case"

I would think that enforcing economic sanctions would be a far more effective use of time and effort.

Shutting down a business = economic sanctions. Blocking domain of a web publication is part of shutting it down.

What do you prefer instead, to make domain registrars enforce sanctions instead of blocking on DNS level? That would quickly make so that no one with Russian passport is able to register a domain no matter how much we are against russia or putin

Because the people writing the laws within the EU are also acutely aware that phrasing this ban too broadly constrains freedom of speech. The way the ban is handed is walking the fine line between impinging freedom of speech and denying a enemy state from waging an information war. Romania had to rerun an election due to Russian inference, this isn’t just a phantom the EU made up to censor opinions it doesn’t like.