feat(backend): Discord OAuth login with DB-backed sessions (#23)

The browser UI signs in with a Discord authorization code grant
(identify + guilds.members.read) instead of a shared password. Guild
membership is the gate; the owner's Discord ID is the only identity
allowed in while registration is closed. Sessions become rows in a
sessions table with opaque random ids — the cookie carries only the id,
looked up and expiry-checked per request — so deleting a row revokes a
session. HMAC cookie signing, its derived key, and WEB_PASSWORD are
gone, and no replacement signing secret is introduced (ADR-0002).

Discord's API base is configurable (DISCORD_API_BASE); the full flow is
tested through the real router against a local stub, including the
form-encoded token exchange Discord rejects if sent as JSON.

backend/internal/store/sessions.go

@@ -0,0 +1,59 @@
+package store
+
+import (
+	"database/sql"
+	"time"
+)
+
+// Session is one browser login: an opaque id the cookie carries verbatim,
+// the Reader it belongs to, and when it stops being valid.
+type Session struct {
+	ID        string
+	ReaderID  int64
+	ExpiresAt time.Time
+}
+
+// CreateSession stores a new session row for reader. The id is generated by
+// the caller (session.NewID) — the store only persists it. Expired rows that
+// were never looked up are swept here: this is the one write every login
+// makes, so the table stays bounded without a background job.
+func (s *Store) CreateSession(id string, readerID int64, ttl time.Duration) (Session, error) {
+	expires := time.Now().Add(ttl)
+	_, err := s.db.Exec(`INSERT INTO sessions (id, reader_id, expires_at) VALUES ($1, $2, $3)`,
+		id, readerID, expires)
+	if err != nil {
+		return Session{}, err
+	}
+	_, err = s.db.Exec(`DELETE FROM sessions WHERE expires_at < now()`)
+	if err != nil {
+		return Session{}, err
+	}
+	return Session{ID: id, ReaderID: readerID, ExpiresAt: expires}, nil
+}
+
+// GetSession returns the live session row for id, or ok=false when the id is
+// unknown or expired. An expired row is deleted on the way out, so the table
+// never grows past sessions that are still valid.
+func (s *Store) GetSession(id string, now time.Time) (Session, bool, error) {
+	var sess Session
+	err := s.db.QueryRow(
+		`SELECT id, reader_id, expires_at FROM sessions WHERE id = $1`, id,
+	).Scan(&sess.ID, &sess.ReaderID, &sess.ExpiresAt)
+	if err == sql.ErrNoRows {
+		return Session{}, false, nil
+	}
+	if err != nil {
+		return Session{}, false, err
+	}
+	if !sess.ExpiresAt.After(now) {
+		_, _ = s.db.Exec(`DELETE FROM sessions WHERE id = $1`, id)
+		return Session{}, false, nil
+	}
+	return sess, true, nil
+}
+
+// DeleteSession revokes one session. Deleting an unknown id is not an error.
+func (s *Store) DeleteSession(id string) error {
+	_, err := s.db.Exec(`DELETE FROM sessions WHERE id = $1`, id)
+	return err
+}