Switch to OIDC for NuGet.org publish tokens

[Flash0ver]

Similar to #6422, but no rush.

There is no deadline / deprecation of classic NuGet tokens, though. Also, we are unaware of recent attacks / abuses.
However, this should make publishing the sentry-dotnet NuGet packages from GitHub Actions more secure.

Announcement: https://devblogs.microsoft.com/dotnet/enhanced-security-is-here-with-the-new-trust-publishing-on-nuget-org/
Documentation: https://learn.microsoft.com/nuget/nuget-org/trusted-publishing