The PR build definition can be found here or by nagivating through an existing PR.
NuGet packages produced from every build of main are auto-published to the NuGet feed https://pkgs.dev.azure.com/dnceng/public/_packaging/dotnet-tools/nuget/v3/index.json
A new version of the VS Code extension can be published with this release definition. You'll have to select the appropriate passing build to publish. This is a one-step process. Once submitted, the new extension will appear in the VS Code Marketplace in about 10 minutes once their internal validations are complete.
The publish/verification script is located in this repo at eng/publish/PublishVSCodeExtension.ps1.
The public GitHub code is internally mirrored here to enable signed builds. You'll likely never need to do anything with this.