[tests] Follow up work for `Workload tests` PR

[radical]

• [x] Installing the workloads for test takes <1min compared to the build workloads step which takes over 4mins. Not worth merging these two steps. ~~On windows CI the workload is built, and installed separate from the existing "Build the workloads step". Consider de-duplicating the work. Also, see https://github.com/dotnet/aspire/pull/4168#discussion_r1604130437~~
• [ ] Add dogfood.ps1
• [ ] More tests, enhance checks (https://github.com/dotnet/aspire/pull/4240)
• [ ] If a new nuget is found in artifacts then remove the corresponding entry from the local nuget-cache
• [ ] Make test class names extraction more robust so it isn't dependent on tests having a fixed prefix
• [ ] Consider renaming TestUsingWorkloads and streamlining the use of this, and InstallWorkloadUsingArtifacts
• [ ] Consolidate the RequiresDocker story across the various test projects (see https://github.com/dotnet/aspire/pull/4168#discussion_r1606930361) - https://github.com/dotnet/aspire/pull/4260 cc @joperezr @eerhardt