I'm not talking about the source control icons, but the blue overlaid icon on the right.

It means there is an alert for the project. If you hover over the icon you get the Source Control tooltip ("Checked In" in the other answer), but if you hover over the title of the project you will get a tooltip with the alert.
A bit late, but for reference as I was looking, I am just converting a solution to a later project and what it appears to mean is that the blue dotted project will produce no output for the current configuration - ie, you are currently building a debug x86 build but there is only a configuration for x64 or release. In the .net8 build I was doing it lacked a list of configurations:
<PropertyGroup>
<TargetFramework>net8.0-windows10.0.17763.0</TargetFramework>
<ImplicitUsings>enable</ImplicitUsings>
<Nullable>enable</Nullable>
<Platforms>x86</Platforms> <--
<Configurations>Debug;Release</Configurations> <--
</PropertyGroup>
so that even though it has separate entries for those project types later on, it wasn't using it.
If you look in the project output you will see that the project was skipped:
========== Build: 3 succeeded, 0 failed, 0 up-to-date, 2 skipped ==========
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