I currently use the link checking plugin to deploy my sites. I came across a problem with the link checker marking a deployment as failed when in fact it worked properly. I believe that your link checker is improperly assuming that the “src” property in the “icons” section is an absolute link ie from the root of the site whereas the specification for site.webmanifest icons says that the link should be relative the location where the site.webmanifest file is located.
In my case I have a hugo site and the icon is in the /static/icons/x.png. The site.webmanifest file is in the /static/icons/ directory. The src property for the icon should be just /x.png. In order to fix the problem I have had to override the src property locally with a src property like /icons/x.png. This is not correct according the specification for site.webmanifest files.