That grey outline is a classic premultiplied-alpha fringe: the semi-transparent edge pixels are carrying the matte color (usually black/grey), and it shows up when the file is decoded and composited. Your ProRes 4444 master likely has premultiplied alpha, and the fringe got baked into the WebM.
Two things to try:
1. In AE, apply Effect > Channel > Remove Color Matting to the logo layers before exporting — it removes fringes from semi-transparent areas.
2. Or render with straight (unmatted) alpha instead of premultiplied — straight channels retain more accurate color information.
Adobe explains the difference here: https://helpx.adobe.com/after-effects/desktop/work-with-footage-items/import-and-interpret-footage-items/importing-interpreting-footage-items.html
If the developers don't need transparency, baking in a solid background kills the issue entirely.