Hard to notice. I can barely see the issue.
Hard to fix. Each app (yes, that includes multiple Adobe apps) will always (yes, always) render the same thing in a slightly different way (because of settings and/or just different render algos).
Let it go :)
You can do File > Export > Artboards to Files and choose JPEG as the file format. This can be recorded in an Action if required, then you could apply the Action to a whole bunch of PSDs using File > Automate > Batch
Export the images as PNG as you would normally, using Export As. Then record an Action to open and export one of the PNG images as WebP. Apply the Action to all the images in a folder using File > Automate > Batch.