I reviewed your template and have the following comments.
template.json should define guids which need to be replaced. You should include every <ProjectGuid> from .*proj files. You can use this PowerShell statement to find all guids Get-ChildItem .\ * -Recurse -File|Select-String '[0-9a-f]{8}-[0-9a-f]{4}-[1-5][0-9a-f]{3}-[89ab][0-9a-f]{3}-[0-9a-f]{12}'.
Add <!--/-:cnd:noEmit --> at the top of all MSBuild files (.*proj files), see (this comment)[https://github.com/dotnet/templating/issues/1195#issuecomment-321344890] for more info
After creation there is a LICENSE file with your name on it. The file should either not be dropped or your name should be removed at least.
Some other things I noticed
One other thing to consider. I noticed that you included the launchSettings.json file. I'm guessing this is because you wire up the projects to talk to each other via their specific ports. One drawback from this approach is that the same port numbers will be used. This should work fine in most cases so it's not a big deal. If a user has two different instances of VS with a different solution in each only one of them will run at a time. I think we have all the features you would need to generate a new port number and then include that as a replacement into the launchSettings.json, see https://github.com/dotnet/templating/wiki/Reference-for-available-macros.
I also found an issue with having to revert the Microsoft.AspNetCore.All version back to 2.0.0 in the web project (.csproj) as per this thread and Mcafee123's answer - https://github.com/dotnet/coreclr/issues/13542.