fix: API Dockerfile — include mcp-servers workspace lib in production

@goodgo/mcp-servers is a workspace dependency used at runtime.
Need to copy its package.json for pnpm install resolution and
its compiled dist/ output into the production image.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

apps/api/Dockerfile

@@ -54,6 +54,7 @@ ENV NODE_ENV=production
 # Install production dependencies fresh (pnpm hoisted node_modules has broken symlinks in Docker)
 COPY --from=deps /app/pnpm-lock.yaml /app/pnpm-workspace.yaml /app/package.json /app/turbo.json /app/
 COPY --from=deps /app/apps/api/package.json /app/apps/api/
+COPY --from=deps /app/libs/mcp-servers/package.json /app/libs/mcp-servers/
 COPY --from=deps /app/prisma /app/prisma
 # Mock husky (git hooks tool) so postinstall scripts run without git
 RUN corepack enable && corepack prepare pnpm@10.27.0 --activate \
@@ -62,6 +63,9 @@ RUN corepack enable && corepack prepare pnpm@10.27.0 --activate \
     && npx prisma generate
 # Copy compiled application
 COPY --from=build --chown=node:node /app/apps/api/dist ./dist
+# Copy compiled workspace lib (runtime dependency)
+COPY --from=build --chown=node:node /app/libs/mcp-servers/dist /app/libs/mcp-servers/dist
+COPY --from=build --chown=node:node /app/libs/mcp-servers/package.json /app/libs/mcp-servers/package.json
 # Prisma schema
 COPY --from=build --chown=node:node /app/prisma /app/prisma
 # Package metadata