Found now some time for troubleshooting...
I am quite confident that the computer inside the vectrex is still working "fine" because when I scope the audio outlet pins (1,4,5) at the Audio Chip IC 208 I can see activity twice and with different pattern when booting with the test cart (1. Vectrex Start Sound, 2. Test Cart Start Melody). After that no activity. Makes sense. Pressing 5 times on button #4 brings me in the Audio Test section of the test cart. And here I can clearly see the pattern when the test is in action for each channel measuring on the assoziated pin. I can also hear a strange (regularly repeating) swinging sound coming out of the speaker which correlates when the test sound is active.
Looks like the amp chip LM386 is faulty now? However I will take care about this later. Just put this on my to do list (haha

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So I moved on with testing the OPAMP chips. Unfortunately when scoping IC304-6 or at J301 I dont get a clear picture anymore. The trigger seems not to work anymore with my scope. Got the same setup as when I have checked the X,Y and Z first time. However the pattern is quite similiar but now I see also a negative amplitude at Y. Furthermore X looks quite the same as Y now. Very strange. Z looks normal.
Not sure but is it possible that the Y and the X signal now are overlapped on each line?
What is also strange the pictures are looking quite the same also at the other pins at IC304 and IC306. Furthermore Pin 3 is flat. I checked whether there is a short to ground but it is not. But I can measure continuity between IC304-3 and IC306-3. Is that normal?