This artifact seems related to the chroma subsampling because it is much more pronounced when HQ option is unchecked, but here the problem arises.
4:2:2 means that only two samples per colour are taken every 4 luma values, and 4:2:0 (or 4:1:1 with a different matrix/order of sampling) that the sample per colour is only one. It's the way video is captured where luma samples are followed by the blue and red differences.
When YCbCr (4:2:2 or 4:2:0) is converted to RGB, Y, the luma, is usually assigned to the green channel, and consequently the green should have a much higher true resolution compared to the red and blue, but here's the problem.
I've made a simple test of text on three different flat backgrounds: blue, red and green.
As you see the green background shows as much artifacts as the red one and (apparently) less than the blue, which is the colour to which the human eye is less sensitive and, because of this, it gets the smallest number of information even in the Bayer matrix of a CCD/CMOS.
Moreover, if the Web Export HQ means 4:4:4, with this option activated there should be virtually no artifacts with any background colour.
How is it?
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png 16 colours / nearest colour

jpg HQ disabled

jpg HQ enabled

png 16 colours / nearest colour

jpg HQ disabled

jpg HQ enabled

png 16 colours / nearest colour

jpg HQ disabled

jpg HQ enabled

Jpeg compression is set to 60% for all.