feat: Add Dockerfiles and docker-compose.yml for full-stack local development

[khushigoel44-afk]

Feature Description

Add Dockerfiles for both server/ and web/ services, along with a root-level docker-compose.yml to orchestrate the entire application stack (Next.js frontend, Express backend, PostgreSQL with pgvector, and Redis 7).

Problem it Solves

Currently, setting up Writers Pub locally requires manually installing and running PostgreSQL 16, configuring the pgvector extension, running Redis 7, and managing multiple terminal instances for the web and server apps. This introduces platform-specific friction and setup errors (e.g., missing pgvector extension as noted in the Troubleshooting guide).

Containerizing the project with Docker Compose allows developers to start the entire environment with a single command (docker-compose up), ensuring a consistent and isolated development setup across all platforms.

Feature Description

Add Dockerfiles for both server/ and web/ services, along with a root-level docker-compose.yml to orchestrate the entire application stack.

Specifically, I will be adding/modifying the following in the repository:

1. docker-compose.yml (root): To orchestrate the Next.js frontend, Express backend, PostgreSQL (with pgvector), and Redis 7.
2. server/Dockerfile & server/.dockerignore: To containerize the Node.js Express backend.
3. web/Dockerfile & web/.dockerignore: To containerize the Next.js frontend.
4. README.md update: To include a new "Running with Docker" section with the single docker-compose up instruction.

[khushigoel44-afk]

I am participating in GSSoC'26 and would like to be assigned to this issue.