feat(backend): Replace Node.js API with .NET 8

This commit completes the migration of the backend service from a Node.js/Express application to an ASP.NET Core 8 Minimal API.

- Re-implemented all API endpoints in C# for improved performance and type safety.
- Updated the Gitea Actions workflow to use the `setup-dotnet` action, `dotnet publish` for building, and now caches NuGet packages.
- Modified the deployment to create an `appsettings.Production.json` file from Gitea secrets instead of a `.env` file.
- Updated the PM2 ecosystem configuration to run the application using the `dotnet` interpreter.

backend/.dockerignore

@@ -0,0 +1,30 @@
+**/.classpath
+**/.dockerignore
+**/.env
+**/.git
+**/.gitignore
+**/.project
+**/.settings
+**/.toolstarget
+**/.vs
+**/.vscode
+**/*.*proj.user
+**/*.dbmdl
+**/*.jfm
+**/azds.yaml
+**/bin
+**/charts
+**/docker-compose*
+**/Dockerfile*
+**/node_modules
+**/npm-debug.log
+**/obj
+**/secrets.dev.yaml
+**/values.dev.yaml
+LICENSE
+README.md
+!**/.gitignore
+!.git/HEAD
+!.git/config
+!.git/packed-refs
+!.git/refs/heads/**