Enable OPS auto-publish in .NET repos

[gewarren]

Describe the issue or suggestion

Enable OPS auto-publish, add a required status check to the live branch ruleset for status-checker, and remove the existing auto-publish GitOps policy, in these repos:

• dotnet/docs
• dotnet/dotnet-api-docs
• dotnet/dotnetfw-api-docs
• dotnet/dotnet-api-docs-temp
• dotnet/docs-desktop
• dotnet/aspnetcore.docs
• dotnet/docs-maui
• dotnet/docs-mobile
• dotnet/docs-archive-pr
• dotnet/docs-tools
• dotnet/docs-actions

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Associated WorkItem - 636393