I wouldn't be concerned.
In German academia, it is rather common to make PhD/postdoc offers informally (i.e. just via email etc.), and the formal process is only completed at a much later point. I know of many cases where people only sign their contract on their first working day (in particular in pre-Corona times, administration wanted to do the signing in person, so if you were in a different place, this would be postponed until you arrived).
On the other hand, even without the contract, you can get a confirmation that you will be hired in the future, once the necessary paperwork is completed.
However, it will be impossible to get such a confirmation without having the required paperwork completed - just imagine that in the course of that, it turns out that you don't have the required qualifications (no PhD, no degree, ... ) - the administration will not sign that they will hire you unless they are sure that this is legally possible.
One thing you can do to speed up at least part of the process - to make sure that you don't "accidentally" miss a qualification (very unlikely) - is to supply all required documents as soon as possible and check that they are sufficient. Even if the process is not completed yet, this should give you additional security that things will not go wrong for formal reasons (again, rather unlikely - they hire people all the time).
Finally, while on the one hand I understand that you want a more formal "safety" that you will get the job, as I said this is rather normal, so no need to worry. But more importantly, you should note that even if you have a contract, within the first 6 months you can be usually fired on short notice and without a reason given (I'm pretty sure this is more or less the same in other places, that there is an initial period where both parties can terminate the employment on short notice, not to speak of places like the US), so even if you have a written offer or even a signed contract, there is still some amount of risk involved, like essentially always in life (unless you have a tenured position).
Edit: Maybe to add a comment, hiring decisions typically have to be approved by the personnel council, and possibly other bodies (equal opportunities, etc.), which can take its time, especially at large universities or research institutes. In addition, if this a position funded by public money, it has to be publicly advertised in one way or the other, and the advertisement has to be open for a certain amount of time (I think 2 weeks at least), before the whole process can even start.
So putting all these processes together,
2 months might well be the minimum time it takes.