feat(api): dockerize backend with compose, migrations-on-start, and run docs

apps/api/Dockerfile

@@ -0,0 +1,27 @@
+FROM node:22-alpine AS base
+RUN corepack enable
+WORKDIR /repo
+
+# Copy workspace manifests for cached install
+COPY package.json yarn.lock .yarnrc.yml ./
+COPY .yarn/ ./.yarn/
+COPY packages/shared/package.json ./packages/shared/package.json
+COPY apps/api/package.json ./apps/api/package.json
+# Copy the other workspace manifests too, so the workspace graph matches the
+# lockfile (otherwise Yarn errors on a mismatch). `focus` still installs ONLY
+# the @solelog/api subtree, so mobile/web deps are not pulled.
+COPY apps/mobile/package.json ./apps/mobile/package.json
+COPY apps/web/package.json ./apps/web/package.json
+
+RUN yarn workspaces focus @solelog/api
+
+# Copy sources
+COPY packages/shared/ ./packages/shared/
+COPY apps/api/ ./apps/api/
+
+WORKDIR /repo/apps/api
+ENV NODE_ENV=production
+EXPOSE 3000
+
+# Apply migrations, then start the server
+CMD ["sh", "-c", "yarn db:migrate && yarn start"]