Update vendored .NET Core project to match project template
What does this MR do and why?
Completes task 2 of #370974 (closed) (add vendored template).
How to set up and validate locally
See !105775 (comment 1198096510) and https://docs.gitlab.com/ee/development/project_templates.html#test-your-built-in-project-with-the-gitlab-development-kit.
MR acceptance checklist
This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.
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I have evaluated the MR acceptance checklist for this MR.
Closes #370974 (closed)
Edited by Jonston Chan