@sharonwhiteley69
Oh, lordy, this kind of problem can be a bit of a challenge, unfortunately.
I have a very similar issue to yours currently in my flat in Cyprus, where there is some kind of leak in the next door kitchen which comes through the wall. This happened a couple of years ago, and it was a challenge to resolve it then as there was nobody living in the flat! We did manage to fix it eventually (we thought), but it has now returned.
Legally, the responsibility for this kind of issue normally lies with the other homeowner, not you, and not the building administration. And in respect of both the damage inside their apartment, and that caused elsewhere. But if it's an uncooperative owner, you might find it difficult to enforce this. You might also find it difficult if you are an absentee owner, and not around all the time to make a nuisance of yourself.
As @Peko Phil says you should definitely talk to your building administrator ASAP. Some are much better than others, so the results can be very variable. Damage in someone's apartment is not their responsibility (so they probably won't "fully handle it"), but they should be able to talk to the owner and put some pressure on them to resolve it. And it's definitely worth getting them involved.
You could also get an attorney. They could write a scary letter informing the homeowner that you'd had a home inspection (so you probably should get a decent firm to do one, and give you a report), and that it has identified your neighbour's apartment as the source of water. And that you have been quoted X thousand euros to repair the damage. And that you are informing them of your findings, and you are holding them responsible for the damage. And if it's not resolved in 30 days, you will start legal action. This can be costly (inspection + lawyer + legal action).
The more practical approach is to assume you'll pay to repair your own damage... and maybe even contribute to repair THEIR leak! If they've shown you their apartment, maybe get them (and the building administrator) to visit yours so they can see how bad the damage is? That might make them a bit more sympathetic. Get a proper construction guy in to look at your studio, and give you a quote to repair all the damage. You can share this with the other owner and the administrator, so they know you have a real problem.
In my Cyprus case, the administrator tried repeatedly (over a month or so) to contact the owner, and when that failed, they eventually authorized us to make forced entry to the other apartment. So I paid for the locksmith, and the plumbing work next door... and the repairs in my apartment. Legally, it should have been the other owner paying for everything... but I figured I'd rather spend the money on repairs than litigation, and the quicker it was resolved, the quicker my flat would be livable! (Sadly, either my plumber didn't do a very good job, or there is a new leak close to it,)