Fix Analyzer.Core NuGet packaging process for dependency package tracking

### Please describe the feature or suggestion.

The nuspec file for Analyzer.Core (/src/Analyzer.Core.NuGet/Analyzer.Core.nuspec) is currently maintained manually. This means NuGet dependencies very quickly and easily become out of date when developers update a NuGet package dependency in code but miss updating the nuspec file.

Instead, a process should be utilized that builds the spec during packaging, so it's always completely accurate.

### Additional context

_No response_