I am less familiar with the ELv2 license, but for an MSP managing the cloud environments of several clients, where is the line of a so called managed service drawn? Is setting up and upgrading Airbyte instances at our customers own cloud environment now prohibited? If this is the case, will we also be able to order licenses on behalf of clients?

Not prohibited at all. The main thing that you cannot do is offer a hosted version of Airbyte that you sell to the public (such as AWS offering their hosted version of Airbyte).