You are right to not want to use "developed" as saying two forms of "develop" in a row like that is jarring.
I'm assuming that there are various levels of development of H2 infrastructure and you are trying to say Germany has the most advanced level of development.
mature - This would apply if "H2 infrastructure" is a single thing that grows as it ages, but for an infrastructure to grow can mean a couple of different things, so it's too vague unless context explains what is meant by H2 infrastructure. Mature also implies that it's "done" advancing or that the rate of advancing is slowing down - not sure if you want to mean this or not.
advanced - I would go with this one. But "most advanced" when used directly in your sentence can mean just "very advanced." So I would say "Germany's H2 infrastructure development is the most advanced."
common - Your sentence would mean that the event "development of H2 infrastructure" happens the most in Germany, not anything about the level of development of its H2 infrastrcture.
prominent - This means that "development of H2 infrastrcture" is most visible compared to other countries (maybe from a helicopter?), but not saying anything about the level of development of that H2 infrastructure.
widespread - THis means that "development of H2 infrastructure" covers most of the area of the country or area you are talking about, but does not say anything about the level of development of that H2 infrastructure.