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

apps/api/.dockerignore

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+node_modules
+.tmp
+data
+drizzle/meta

apps/api/.env.example

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+DATABASE_URL=file:./data/app.db
+BETTER_AUTH_SECRET=change-me-to-a-long-random-string
+BETTER_AUTH_URL=http://localhost:3000
+PORT=3000

apps/api/Dockerfile

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+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"]