Backend Phase A: foundation, migrations, Docker setup

- Go backend skeleton: config (caarlos0/env), slog JSON logging,
  pgxpool store, HTTP server with graceful shutdown.
- httpapi: render helpers, Problem errors, middleware chain
  (requestID / logging / recover / CORS), /healthz and /readyz.
- Migrations: full initial schema (users, sessions, lists,
  list_members, items, op_log SOURCE OF TRUTH, item_names) +
  golang-migrate runner binary using source/iofs (embedded).
- Docker: multi-stage Dockerfile (Go 1.26 -> distroless nonroot),
  builds both server and migrate binaries.
- deploy: docker-compose (caddy + backend + migrate + postgres:16),
  Caddyfile (auto-HTTPS), .env.example, pg extensions init script.
- AGENTS.md: project context + roadmap for AI agents.

Verified: image builds, both binaries run in container (smoke test).

backend/internal/store/db.go

@@ -0,0 +1,32 @@
+// Package store wraps database access (pgxpool) for the backend.
+package store
+
+import (
+	"context"
+	"fmt"
+
+	"github.com/jackc/pgx/v5/pgxpool"
+
+	"github.com/mitbringsl/backend/internal/config"
+)
+
+// New creates and configures a pgx connection pool, then pings the DB to verify access.
+func New(ctx context.Context, cfg *config.Config) (*pgxpool.Pool, error) {
+	pcfg, err := pgxpool.ParseConfig(cfg.DatabaseURL)
+	if err != nil {
+		return nil, fmt.Errorf("parse database url: %w", err)
+	}
+	pcfg.MaxConns = cfg.DBMaxOpenConns
+	pcfg.MinConns = cfg.DBMaxIdleConns
+	pcfg.MaxConnLifetime = cfg.DBMaxLifetime
+
+	pool, err := pgxpool.NewWithConfig(ctx, pcfg)
+	if err != nil {
+		return nil, fmt.Errorf("create pool: %w", err)
+	}
+	if err := pool.Ping(ctx); err != nil {
+		pool.Close()
+		return nil, fmt.Errorf("ping db: %w", err)
+	}
+	return pool, nil
+}