Indeed, and that's why search relevance is important.
We can talk about the Importance Of This until we die of old age. Google failed us, Google is Borg, Yandex is FSB, Bing is ... Bing, etc. However, the fact that there is a problem to be solved and It Is Important doesn't mean that the EU will solve it. If anything, it's just the set-up for another political play that will have damaging consequences to the internet as a whole, just like GDPR, EU's poster-child "internet project".
They made GDPR just strong enough legislatively to be annoying, but not strong enough to actually change anything. Companies can still store EU citizens' data anywhere they want and do whatever they want. There's no insight into this. It is an unenforceable law and the only artifact of it existing is that I have to have "I don't care about cookies" installed, so that Avast Antivirus can eventually decide to silently collect and sell on my data.
For all intents and purposes OpenWebSearch is most likely not meant to succeed at anything either, and is just going to be a political stepping stone towards legislature that will be awkward and make the internet worse for all users. EU has a long history of creating or hanging onto laws that betray a misunderstanding of how the digital age works, how the internet works, how data can be copied or moved around for free.
Here's an example. Every country in Europe has some sort of legal construct in place that will prevent you from secretly recording a conversation you're having and uploading it to the internet. So for example, take Austria. They accomplish it by preventing you from publishing it on the internet. However, they don't prevent you from recording it. There are laws against secretly recording a conversation you are not a part of, but there's no such law for the situation when you are part of the conversation. So you can record and upload, just not publish. However, you can get on a train and go to a different country which has laws that prevent you from recording, but has no laws against publishing. Then you're in the clear. Or you can just use a VPN so that it looks like you uploaded and published it from the other country. Or you can just upload to YouTube, which will not show where the thing was published from - and claim that you did so during your tourist visit to Vietnam or whatever. And if someone brings a civil lawsuit? Good luck trawling the Vietnamese legal system for clues about that specific issue. Hope you know this rare language with virtually no legal experts who at the same time speak Vietnamese and your particular local European language. The costs would be on the order of tens of thousands at least, which is out of reach for anyone but the wealthiest EU citizens.
Want more? Egregious copyright related laws are known by everyone.
So are dns blocks of shunned sites. Or the recent Austrian project to block cloudflare IPs which literally broke the internet.
The fact such laws are still in place from before the internet - or are even still being put out - and are effectively unenforceable while making the internet worse for everyone - makes it clear that the governments in place simply have a misunderstanding of how the internet works.
None of that will stop politicians from coming up with BS excuses breaking the world with fever-dream laws in order to push their latest political agenda. The real question is: if such clearly unfit legislature is being put in place for political folly in industries we understand - how much of that is happening in industries we don't understand? Health Care, Food, Agriculture, Civil Engineering, Patent Law, and so on. My guess? You can tell what my guess is.
As for Open Web Search, what everyone should really be asking themselves is: ok, so what's the scam that's going to be pulled here?