Could you make sure your .csproj file looks a little bit like this?

<Project Sdk="Microsoft.NET.Sdk.Web">

  <PropertyGroup>
    <TargetFramework>net5.0</TargetFramework>
  </PropertyGroup>

  <ItemGroup>
    <PackageReference Include="Swashbuckle.AspNetCore" Version="5.6.3" />
  </ItemGroup>

</Project>

The problem may be with the missing of the nuget packages. I had the same problem.
Try these steps:

1. Install the matching Nuget version from https://www.nuget.org/downloads
2. If you already created a project, try adding --force after the new sln and web api creation commands to update the files.

I was trying to build an API using dotnet CLI as well, for a couple of days now. Ended up getting no answer from microsoft, or another source of info.

Anyways, the only way I made it work was unstalling .NET SDK 5.0.203 (Latest version for the time being), and installing .NET SDK 5.0.101, and thats it, new api command works flawlessly.

Just got the same issue on a clean machine. I managed to fix it running the command:

dotnet nuget add source --name nuget.org https://api.nuget.org/v3/index.json

After that, create/restore your project and it should work.

source