You just need to find someone else with a known good Camera/VTX/monitor to compare with.
I had problems with my first FPV setup, turned out my goggles had an intermittent fault, but with only one set I was baffled, I ended up buying a second set of goggles to troubleshoot and found the problem straight away - sine then I make sure I have two of everything so I can troubleshoot if something isn't working (ie swap cam/vtx/goggles to find a combination which works and then you can identify the faulty part).
That's a great idea, you just need to try your monitor with one of their camera/transmitters and vice versa, once you have a known good setup its much easier to work out what's going on, it could just be a bad connection/wire.
I checked and your camera is 5v so is vtx, as that was my first guess (a 12v camera on 5v can just give out black signal).
Sounds like it has to be the camera, not the vtx or the goggles, since the camera settings OSD is showing up in the goggles. My guess would be that 7.4V may be too high for the camera. You might try to put a 5V BEC between the battery and camera. Does the camera give an input voltage range, or does it just say 5V input?
Edit: I just noticed You are powering the camera through the vtx so I'm not sure what to think. You could check the voltage coming out of the vtx with a multimeter.
Per the camera spec, it supports 5-17V. I'm at a loss, other than the camera just being busted.
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Yeah, this is a perplexing one. You must be right, something wrong with the camera.