Your problem is not a novelty. Legacy versions of Photoshop have rendered partially transparent items differently against an opaque background layer and against the transparency checkerboard. It's not an illusion caused by the checkerboard, but the rendering boosts transparency and causes pixelation if there's nothing behind.
This is my bottom layer:
The right half contains nothing visible, there's only the transparency checkerboard. The left half is not transparent, it contains a screenshot of the transparency checkerboard.
A top layer is inserted and a couple of horizontal brush strokes are drawn with a maximally soft brush; the hardness = 0:
Both strokes have the same brush width, but in the upper stroke the brush spacing is sparse. In the lower stroke the brush spacing is adjusted to the allowed minimum =1%. The transparency of the strokes is boosted substantially in the right half. Opaque is still opaque, but the transparent color seems to fade much faster if there's nothing in the background. With high zoom in one can see in the right half some irregular pixelization. I guess you have also noticed it:
In the next image the bottom layer is temporarily closed to show that the brush strokes are the same in the left and right halves.
But which is the right way to render? I believe that the rendering of partially transparent items against an empty background is wrong in Photoshop. Or actually it's useless if one likes to see how the image would be rendered elsewhere. Staying only inside Photoshop it could be called a feature. That's because rendering against a solid background becomes the same as rendering against nothing if one changes to advanced color settings "Blend RGB colors using Gamma =1.00"
I wouldn't call this a fix. Using Gamma=1 for RGB blending is even more OFF if one wants to see how other applications render the same image.
Let "Blend RGB colors using Gamma =1.00" stay unchecked and export the image as PNG and save it also as PSD. When one opens the PSD and the PNG in Krita and Affinity Photo they both look the same. Also both halves are rendered equally and it's like the left half was in Photoshop when "Blend RGB colors using Gamma =1.00" was unchecked. Paint.NET accepted only the PNG, but also there both halves were equal and the same as in Photoshop against background. An example:
This is the PSD opened in Krita. In the right there's Krita's transparency checkerboard.
Opening the PNG in Photoshop gives the same transparency boost to the right half like it was when the image was just created as PSD in Photoshop.