A good test would be to run a single 100% sRGB red pixel through your image processing pipeline, and then inspecting the resulting PNG file in a hex editor to see what value is encoded.
You can also visit this web page to actively test each web browser’s respect for embedded ICC profiles: https://www.gballard.net/psd/go_live_page_profile/embeddedJP...
The WebKit blog from 2016:
WebKit color-matches all images on both iOS and macOS. This means that if the image has a color profile, we will make sure the colors in the image are accurately represented on the display, whether it is normal or wide gamut. This is useful since many digital cameras don’t use sRGB in their raw format, so simply interpreting the red, green and blue values as such is unlikely to produce the correct color. Typically, you won’t have to do anything to get this color-matching. Nearly all image processing software allows you to tag an image with a color profile, and many do it by default.
[1]: https://webkit.org/blog/6682/improving-color-on-the-web/