fix: add backend .dockerignore and fix build stage dependencies

[Doiae9]

Summary of Contributions

1. Optimized Docker Build Context

• Added backend/.dockerignore: Excluded heavy and sensitive directories/files (such as node_modules, dist, coverage, .env*, *.log, and src/generated) from being sent to the Docker daemon. This significantly drops the build context size and mitigates the risk of leaking sensitive environment variables into the build layers.

2. Fixed Backend Dockerfile Multi-Stage Build

• Dependency Resolution: Adjusted the builder stage to execute a full npm install instead of restricting dev dependencies. This ensures that essential CLI tools required for compilation (like TypeScript and Prisma) are fully available during the build phase.
• Prisma Schema Inclusion: Added the COPY prisma ./prisma directive into the builder stage to resolve a critical build failure where the compilation script could not locate the required database schema file.
• Production Optimization: Maintained the --omit=dev flag in the final runner stage to keep the production container image as lightweight, secure, and lean as possible.