Problem with C20NE

Hi, a few days ago I bought the Astra F Cabrio with the 2.0i engine (8 valves, year 1993) and wondered about the behaviour during the acceleration: up to about 2500 it accelerates perfectly, so at the latest from about 3000 rpm does not do too much if one passes the accelerator pedal further, or with a clear delay. So from about 4000 it turns free up again, until far over 5000 where then is switched up at the latest. But the engine also does not stutter in the mentioned range, od otherwise it sounds kind of sick, it just feels like a rotating memento, as if just the expected performance is not available immediately, or comes with delay. It seems to me as if the injection there either does not provide enough fuel, or something like that. Is this part maybe down for the ASU, or do I need an update of the software (if there is one for the engine at all)? can anyone tell me something about it? And if there is a Möglic I don’t mean an advanced tuning, but really just a few tips that you can test just as often, like chip tuning, air filter or something like that (sorry, unfortunately, have little idea of the topic)