Embedded ICC profiles aren’t the only way to specify an image’s colorspace. Depending on the image format, colorspaces may be defined through additional metatags.
PNG files have
sRGB chucks. There are the XMP tags
In practice, I’m not sure how much this matters. macOS seems to correctly handle the PNG chunks, but Affinity Photo doesn’t. With such inconsistent tooling support, it might be better to strip these tags and use an embedded profile, or omit one when that makes sense (Modern Browsers Assume Untagged Images and Colors Are sRGB).