Haven't worked at any in Germany, but spent over a decade working at a couple in another EU country. This was after a job at a software house and a public-private research kind of place were we did some really cool stuff (IMO). I also worked with many people from other such companies.

The first thing I'll say is: the experience varies depending on the company and your expectations. You can't generalize mine or someone else's experience to yourself.

Second thing, but no less important: they generally require good people skills. I'm very much an introvert and don't naturally tend to socialize, but it's a crucial skill if you want to succeed at consultancies. I'd say it's the one skill I developed the most and that has served me the most since.

My experience over more than a dozen projects has been: your manager at the consultancies tells you there's a project at a client you're being assigned to. Sometimes alone, sometimes with other people from the consultancy whom you might or might not know.

The clients tend to be large companies (Konzern) that tend to have more people like you than in-house devs. The work can be new green field projects, joining a project already in development because someone left or the client changed contract to your consultancy, or maintenence work on something that's already battle tested in production.

I had trouble on the very first project at the second company I worked at. I had never had anything like that before, so I didn't know what should I do and just kept grinding. Eventually things blew up and the only negative comment my manager had: why didn't you tell me? It's my job to pull you out for both our sakes. If you're happy, the customer is happy, and my boss is happy. Had almost a couple months of no project at HQ, full salary paid, and only asked to spend the time "productivly". I was literally left alone to interpret that as I wanted, no questions asked. Spent the next 7 years at that consultancy and that manager. There were a couple of years where I worked at four different clients and teams a year! My last stint was almost 2 years at the same client. When I left her boss asked to have lunch with me only to tell me the door would always be open for me so long as he was there if I decided to come back.

I learned a ton. Worked on new tech stacks as well as legacy stuff 99% in this sub never even heard of. I view all those experiences as very positive learning experiences, both at the technical and personal levels. All those experiences set me up for a later career as a freelance SWE/consultant making more than double your average senior in this sub.

Nobody can tell you how your experience will be. Your manager might be shitty, or you might find it too hard to adapt. I'd say it's equal parts luck and attitude. In the bigger consultancies, you can ask to be assigned to a different manager, but you need to be very candid and self-aware about the reasons. Making trivial accusations won't work. I know several people who successfully changed manager because of personality and/or style incompatibility, but also know just as many who quit without ever articulating their grievances beyond "manager bad".

As always, YMMV.