It is not Aurelia that is the problem, it is the templates. The script references seem to be incorrect.
Try this:
au new --here
Open the \Views\Home\Index.cshtml
and change the ‘Development’ scripts to this:
<environment names="Development">
<script type="text/javascript" asp-src-include="~/dist/*.bundle.js" asp-append-version="true"></script>
<script type="text/javascript" asp-src-include="~/dist/*.chunk.js" asp-append-version="true"></script>
</environment>
Now:
dotnet run
Open: https://localhost:5001/
Now it works.
It should just work out of the box.