I also ran into this issue recently while deploying a ClickOnce application.
I found the solution for this problem on the CefSharp Issues page 1314 by the user @CRoemheld at this link here.
As noted elsewhere, ClickOnce will only bundle up managed .DLL's as part of its deployment process.
But we also need to include the native CEF DLL's as part of our app.
It doesn't look like there is an easy way to do this through the Visual Studio UI (I tried), but you can do it easily by manually modifying the .csproj file to include the following.
Open up your .csproj file and append the following snippet before the final </Project>
identifier.
<ItemGroup>
<Content
Include="$(SolutionDir)packagescef.redist.x86.3.2526.1362CEF***" Exclude="$(SolutionDir)packagescef.redist.x86.3.2526.1362CEFx86***;$(SolutionDir)packagescef.redist.x86.3.2526.1362CEFlocales***.pak">
<Link>%(RecursiveDir)%(Filename)%(Extension)</Link>
<Visible>false</Visible>
</Content>
</ItemGroup>
<ItemGroup>
<Content Include="$(SolutionDir)packagescef.redist.x86.3.2526.1362CEF**en-GB.*;$(SolutionDir)packagescef.redist.x86.3.2526.1362CEF**en-US.*">
<Link>%(RecursiveDir)%(Filename)%(Extension)</Link>
<Visible>false</Visible>
</Content>
</ItemGroup>
<ItemGroup>
<Content Include="$(SolutionDir)packagescef.redist.x86.3.2526.1362CEFx86***">
<Link>%(RecursiveDir)%(Filename)%(Extension)</Link>
<Visible>false</Visible>
</Content>
</ItemGroup>
<ItemGroup>
<Content Include="$(SolutionDir)packagesCefSharp.Common.47.0.4CefSharpx86**CefSharp.BrowserSubprocess.*">
<Link>%(RecursiveDir)%(Filename)%(Extension)</Link>
<Visible>false</Visible>
</Content>
</ItemGroup>'
Once you do this, within Visual Studio, on the publish tab, when you click the "Application Files" button
You will see the required CEFSharp dependencies that will be deployed with the app.
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