What the conversion actually changes
The WebP is decoded to pixels and written back out as a PNG. Transparency is preserved, because PNG supports an alpha channel.
PNG uses lossless compression, so the pixels stored in the resulting file are exactly the pixels your browser decoded from the WebP. Nothing is blurred, softened or further degraded by this step. That also makes it safe for logos, icons, screenshots and anything with sharp edges or flat colour, which is where lossy formats tend to show their weaknesses most clearly.