feat: add Docker support and compile shared package to dist

- Add multi-stage Dockerfile for server containerization
- Add .dockerignore to exclude unnecessary files from build context
- Switch shared package from source to compiled CommonJS output (dist/)
- Server dev/build scripts now build shared package first
- Fix deep imports to use @calchat/shared barrel export
- Update CLAUDE.md with Docker and shared package documentation

CLAUDE.md

@@ -26,10 +26,15 @@ npm run lint -w @calchat/client         # Run ESLint
 npm run build:apk -w @calchat/client    # Build APK locally with EAS
 ```
 
+### Shared (packages/shared)
+```bash
+npm run build -w @calchat/shared        # Compile shared types to dist/
+```
+
 ### Server (apps/server) - Express.js backend
 ```bash
-npm run dev -w @calchat/server          # Start dev server with hot reload (tsx watch)
-npm run build -w @calchat/server        # Compile TypeScript
+npm run dev -w @calchat/server          # Build shared + start dev server with hot reload (tsx watch)
+npm run build -w @calchat/server        # Build shared + compile TypeScript
 npm run start -w @calchat/server        # Run compiled server (port 3000)
 ```
 
@@ -53,6 +58,7 @@ npm run start -w @calchat/server        # Run compiled server (port 3000)
 | | react-native-logs | Client-side logging |
 | | tsdav | CalDAV client library |
 | | ical.js | iCalendar parsing/generation |
+| Deployment | Docker | Server containerization (multi-stage build) |
 | Planned | iCalendar | Event export/import |
 
 ## Architecture
@@ -318,6 +324,8 @@ src/
 
 ### Shared Package (packages/shared)
 
+The shared package is compiled to `dist/` (CommonJS). All imports must use `@calchat/shared` (NOT `@calchat/shared/src/...`). Server `dev` and `build` scripts automatically build shared first.
+
 ```
 src/
 ├── index.ts
@@ -530,6 +538,14 @@ docker compose up -d                  # Start Radicale CalDAV server
 ```
 - Radicale: `localhost:5232`
 
+### Server Docker Image
+```bash
+# Build from repo root:
+docker build -f apps/server/docker/Dockerfile -t calchat-server .
+docker run -p 3000:3000 --env-file apps/server/.env calchat-server
+```
+Multi-stage build: compiles shared + server in build stage, copies only `dist/` and production dependencies to runtime stage. `.dockerignore` excludes `node_modules`, `dist`, `apps/client`, `.git`, `.env`, `*.md`.
+
 ### Environment Variables
 Server requires `.env` file in `apps/server/`:
 ```