@Brunnis Hello Brunnis, I am glad you had a quick look at my results. I have high respect for your work.

I know something must went wrong on my test, as the outcome wasn't consistent and I didn't know the actual delay for input and output devices or even used wrong emulator settings. I expected some sort of delay and just wanted to know how my personal setup works. Currently, there the only way to play on CRT for me is to use that converter.

Quick test of GAMEPAD and CONVERTER

I did a quick test on my USB Fightstick on my PC without RetroPie.

Test 1 does not involve any display. It was just to see how long the LED light on the stick needs to turn on after pressing a button. This is hard to tell, as I can't say for 100% sure when the actual press of button sends a signal. At least the converter, monitor and usb aren't involved here.
Result: 1 or 2 frames of 240 fps, which translates to 0.25 to 0.5 frames at 60 fps (right?).

For Test 2 I used my daily Linux PC with 144 Hz HDMI monitor (without converter). jstest-gtk on Ubuntu was used to visualize a press button on display.
Result: I think 4 frames of 240 fps footage in addition after the LED is lighting up. That translates to 1 frame delay at 60 fps.

At Test 3 I connected same PC to the CRT PC monitor via HDMI to VGA converter. Same jstest-gtk was used as previous test.
Result: 6 or 7 frames at 240 fps footage after the LED is lighting up. Which translates to about 1.5 or 1.75 frames at 60 fps.

Conclusion:

The arcade stick seems to add 1 or 1.5 frame delay on its own, which would mean 16.7ms or 25ms. If Test 2 and 3 are compared, the converter seems to add 1.5 or 1.75 frame delay on its own, which would mean 25ms or 29.2 ms. So, both together are in total adding up approx. about 3 frames or 50 ms latency.

Do you think the autofire/turbo-2 function of arcade stick could send too many key press events, so the emulator or driver gets too busy? Could this have an effect? What do you think about all of this? Does these sound reasonable?

And, should I also just copy the posting to Reddit?