Creating a new release and deploying the package to Nuget are administrative tasks and require that you have admin rights to the dotnet-sdk repository.
Periodically (based on the frequency of this workflow), the source-generator repository will ingest the latest version of GitHub's OpenAPI spec and generate a new version of this SDK. If there is a diff, a PR (similar to this one) will be generated.
When reviewing the PR, analyze the diff and determine whether the changes are breaking (for which a major version number must be incremented), feature additions (for which a minor version number must be incremented), or bug fixes or docs changes (for which a patch number must be incremented). For more details about how to select an appropriate semantic version, see semver.org. In many/most cases, due to the scale of GitHub's specification and the rate of change on it, the diff will be large and the changes will be technically breaking. This will mean incrementing a major version number.
When changes are analyzed, change the PR title appropriately (see this PR for an example) and merge it. Then go to repository releases, tag the release with the chosen version, title it with the chosen version, use the "Generate release notes" button to see what PRs will be included in the release, and manually edit the release notes grouping the changes under the headings Features, Fixes, Maintenance, and Documentation when appropriate. After clicking "Publish Release", the new version will be available for use!