Hello,
you are not using the official version of osTicket, but the German modified version.
In this version there are many enhancements and some reprogramming of the core functions.
One of them is a significant improvement of the search function and I can say that it works as it should for me.
If you need help, please post in the German forum.
If you want, you can also check the behavior in our online demo.
PS: I deliberately do not use links to the project, as it is not wanted and I do not want to advertise.