Yes, Arteta was appointed as Arsenal's coach since 22 Dec 2019 and his contract ends until 30 June 2027, not to mention if there is a contract extension. So yes, Arteta already understands Arsenal's characteristics and needs very well. It's just that, unfortunately, Arsenal has only won a few trophies with Arteta, but Arsenal still keeps this coach.
I guess Arsenal will get a contract extension. Even if Arteta still can't win EPL trophy, he is quite successful managing Arsenal. At least, Arteta almost won the EPL trophy several times.