How to get highest possible JPEG image quality - H7+

I found only slight image quality increases with JPEG image quality settings and I am wondering what is the bottleneck for obtaining the highest possible image quality out of the H7+ with OV5640 sensor.
for instance, from JPEG quality 50 (this is a crop from a lens test chart):

to JPEG quality 85 (above that it is unstable):

So I am wondering what is holding the quality back, because I am used to more detail at this resolution.

These images are saved with an exposure time of 500 ms and a gain of 0.5 dB, so there should not be a problem here.
The lens is not soft - the blur would appear different. It looks like low JPEG quality but it isn’t, since I saved it at he highest quality (and I checked: file size increases with JPEG quality). Is there some bad chroma sub-sampling (what are the settings anyway?). Is it the fact that the sensor is sampled at RGB565, and that’s why see the color squares bleeding more than the black bars? It’s not over-sharpening, some parts are blurred, some parts look aliased. However, I saw the same with Bayer pixformat (but I was saving the image from the IDE live feed) and grayscale.

Have you tried saving the image file as a BMP and comparing?

There’s no hold back for the H7. We feed the RGB565 image into the jpeg compressor and turn RGB565 into YUV with very good precision for JPEG. However… our goal is not spectacular image quality.

Thanks. I could not see a noticeable improvement in BMP files compared to JPG, both generated from a pixel format of RGB565. It seems this is an inherent limitation of the discontinued imaging chip.