What does survive reboot is: during a playing video -> Setup -> Video settings -> stretch to 16:9
Then the video looks good, but gui is still on 4:3 mode (ugly stretched).
If this option is set to a value other than normal, it will also affect the calibration and will be completely bad.
So, please do not use manual aspect ratio override, because calibration alone will solve this. Calibration will set the video and GUI in sync.
For us, that’s the point now, because that’s how it can’t happen that the video is good and the GUI is bad. Either both are good or not. 
Anyway, I managed to find a solution to the problem, though not the way I thought.
The disp_cap file needs to be edited. Inexplicably, the resolution is not recognized if it only includes 576cvbs:
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But, if disp_cap has been edited, it will already appear:
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(My display is already pre-calibrated, of course it won't look like this on your side in the first round, the edge of the image will hang over everywhere.)
If you see the resolution here, the calibration data will also be saved and will not be lost after a reboot.
Contents of the new disp_cap file:
And that's all. 
If you have edited the file, you will need to restart the device and then you can start the calibration, which will not be lost now.
Be careful not to accidentally switch to 720x480i60hz if possible, because I don't think European CRT TV with 60Hz will be able to do anything.