I figured out the quirks of SAI, IrfanView and cwebp and eventually I got PNG with unfuxxed alpha exported and then converted to webp nicely with the google's util.

Seems that SAI outputs incorrect alpha channel data in the PNG export, you need to flatten the image prior to export to correct that.

IrfanView supports WEBP format BUT it doesn't support saving the transparency, nor does it actually support transparency of the WEBP format correctly, it igroner intermediate alpha values, that gave me some headache as I thought the output was wrong from the cwebp until. I downloaded a known good webp with alpha to test and it showed same behaviour as my own file thus I concluded things are proper on my end.

Then I sent the file to some of my friends over Telegram and it worked :D

I will create a nice stickersheet for myself (and to some friends too) eventually.