Yes that's indeed great and I have contributed to OSM, but even for places with tags in multiple languages the search still didn't work great.

Perhaps it's been improved, but I think Organic Maps first searches for the primary name tag first and only later name:es or name:ca. But that means that when searching in Spanish in Valencia (where the name tags are in Valencian/Catalan), it would often give me results outside of Valencia but that would have the name of what I was looking for.

That's not impossible to improve, but it's difficult to get those things consistently right. Google knows so much about its users it can make really accurate predictions about which results are most relevant.

But what's for me way more significant is that OSM is quite unforgiving when it comes to typos or slightly inaccurate spelling. Organic Maps has that problem and openstreetmap.org as well. As an example: there is a part of the city called l'Eixample. If you search for l'Eixample on OSM you will find it no problem: https://www.openstreetmap.org/search?query=l'Eixapmle

But if you forget the apostrophe, lEixample, or if you switch around the m and p, l'Eixapmle, you get no results: https://www.openstreetmap.org/search?query=lEixample

For me that is really frustrating when I'm outside somewhere and have to quickly look up some place on my phone. Most of the time I can still find it with organic maps, but it can definitely be more cumbersome than with google maps.