Refactor database implementation to use PostgreSQL instead of MongoDB (#289)

Fixes #228

## Motivation and Context

See #19

## How Has This Been Tested?

- Run locally
- Run in docker compose
- Run infra in minikube
- Unit and integration tests all passing :)

## Breaking Changes

Yes: users will not be able to access any data they used to have in
custom mongodb. We are accepting this breaking change, given the
registry is in experimental development status.

## Types of changes
<!-- What types of changes does your code introduce? Put an `x` in all
the boxes that apply: -->
- [ ] Bug fix (non-breaking change which fixes an issue)
- [ ] New feature (non-breaking change which adds functionality)
- [x] Breaking change (fix or feature that would cause existing
functionality to change)
- [ ] Documentation update

## Checklist
<!-- Go over all the following points, and put an `x` in all the boxes
that apply. -->
- [x] I have read the [MCP
Documentation](https://modelcontextprotocol.io)
- [x] My code follows the repository's style guidelines
- [x] New and existing tests pass locally
- [x] I have added appropriate error handling
- [x] I have added or updated documentation as needed

## Additional context

I have not implemented connection pooling support for simplicity, and
because cloudnative-pg already provides built-in connection pooling with
pgBouncer so if we want it later we can switch to this endpoint easily.

internal/database/migrations/001_initial_schema.sql

@@ -0,0 +1,58 @@
+-- PostgreSQL schema for MCP Registry
+-- This schema uses a hybrid approach with relational tables for core entities
+-- and JSONB columns for complex nested data structures
+
+-- Enable UUID extension
+CREATE EXTENSION IF NOT EXISTS "uuid-ossp";
+CREATE EXTENSION IF NOT EXISTS "pg_trgm";
+
+-- Servers table - core server information
+CREATE TABLE servers (
+    id UUID PRIMARY KEY DEFAULT uuid_generate_v4(),
+    name VARCHAR(255) NOT NULL,
+    description TEXT NOT NULL,
+    status VARCHAR(50) DEFAULT 'active',
+    
+    -- Repository information stored as JSONB for flexibility
+    repository JSONB,
+    
+    -- Version details
+    version VARCHAR(255) NOT NULL,
+    release_date TIMESTAMP WITH TIME ZONE DEFAULT NOW(),
+    is_latest BOOLEAN DEFAULT true,
+    
+    -- Packages and remotes stored as JSONB arrays
+    packages JSONB DEFAULT '[]'::jsonb,
+    remotes JSONB DEFAULT '[]'::jsonb,
+    
+    -- Metadata
+    created_at TIMESTAMP WITH TIME ZONE DEFAULT NOW(),
+    updated_at TIMESTAMP WITH TIME ZONE DEFAULT NOW()
+);
+
+-- Indexes for performance
+CREATE UNIQUE INDEX idx_servers_id ON servers(id);
+CREATE INDEX idx_servers_name ON servers(name);
+CREATE UNIQUE INDEX idx_servers_name_version ON servers(name, version);
+CREATE INDEX idx_servers_latest ON servers(is_latest) WHERE is_latest = true;
+CREATE INDEX idx_servers_status ON servers(status);
+
+-- GIN indexes for JSONB fields
+CREATE INDEX idx_servers_repository_gin ON servers USING GIN(repository);
+CREATE INDEX idx_servers_packages_gin ON servers USING GIN(packages);
+CREATE INDEX idx_servers_remotes_gin ON servers USING GIN(remotes);
+
+-- Function to update the updated_at timestamp
+CREATE OR REPLACE FUNCTION update_updated_at_column()
+RETURNS TRIGGER AS $$
+BEGIN
+    NEW.updated_at = NOW();
+    RETURN NEW;
+END;
+$$ language 'plpgsql';
+
+-- Trigger to automatically update updated_at
+CREATE TRIGGER update_servers_updated_at 
+    BEFORE UPDATE ON servers 
+    FOR EACH ROW 
+    EXECUTE FUNCTION update_updated_at_column();