Hi Mario,
Question are:
Can you confirm that this is first jhana?
Jhana are defined, in part, as suffusive. (They also come to be personally experienced as suffusive). Therefore it's really useful that you detect the abdomen is not yet suffused by piti. When the jhana suffuses, eventually you will experience this a couple more times and I think that personal experience will let you confirm for yourself. That you already detect the location of where piti is and is not seems useful in my view.
Or maybe it's just a state where the mind kind of makes contact with the jhana, without really being there in a stable way?
I think the effort one makes to collect all sensation and attention into piti is an activity during which the mind does 'contact' aspects that are arising with the effort. For example, there may be apperception of something like lights or light and then the discursive mind may contact that as "unusual" and start questioning and commenting, "What is that?" or "huh?" and "is this jhana?"
Or maybe something else at all?
Always possible. So long as the mind doesn't make up stories about what is happening, then one is making their way to jhana in the steady effort to sustain the mind at piti. If one gets wrapped up in a cognizing about what the mental faculty is experiencing (such as labeling the lights as "special" or something), then one is postponing the effort and the outcome of jhana.
These are just my thoughts. You exploration of your own experience is paramount. You can also review anapanasati and see how your experience lines up word for word or not.