feat(backend): stateless HMAC session cookies for the web UI

Adds sessionKey/signSession/verifySession primitives and
setSessionCookie/clearSessionCookie helpers in a new backend/session.go.
Sessions are derived from API_TOKEN via HMAC-SHA256 with domain
separation (sessionKeyPurpose), so there is no session table and
rotating the token invalidates every outstanding cookie at once.
No routes or handlers yet — that's task 5.

backend/session.go

@@ -0,0 +1,89 @@
+package main
+
+import (
+	"crypto/hmac"
+	"crypto/sha256"
+	"crypto/subtle"
+	"encoding/base64"
+	"net/http"
+	"strconv"
+	"strings"
+	"time"
+)
+
+const (
+	sessionCookieName = "mangabm_session"
+	// 60 days: long enough that a phone stays logged in between reading spells.
+	sessionTTL = 60 * 24 * time.Hour
+	// Domain separation, so the session key can never collide with any other
+	// use of API_TOKEN. Changing this string logs everyone out.
+	sessionKeyPurpose = "mangabm-web-session-v1"
+)
+
+// sessionKey derives the cookie-signing key from the API token. Sessions are
+// stateless — there is no session table — so rotating API_TOKEN invalidates
+// every outstanding cookie at once.
+func sessionKey(apiToken string) []byte {
+	sum := sha256.Sum256([]byte(apiToken + sessionKeyPurpose))
+	return sum[:]
+}
+
+// signSession encodes "<expiryMs>.<base64url HMAC(expiryMs)>".
+func signSession(key []byte, expiryMs int64) string {
+	payload := strconv.FormatInt(expiryMs, 10)
+	return payload + "." + sessionMAC(key, payload)
+}
+
+func sessionMAC(key []byte, payload string) string {
+	mac := hmac.New(sha256.New, key)
+	mac.Write([]byte(payload))
+	return base64.RawURLEncoding.EncodeToString(mac.Sum(nil))
+}
+
+// verifySession checks shape, then expiry, then the signature — in that order.
+// The signature comparison is constant-time; the checks before it only look at
+// data the holder already supplied, so their timing leaks nothing.
+func verifySession(key []byte, value string, nowMs int64) bool {
+	payload, sig, ok := strings.Cut(value, ".")
+	if !ok {
+		return false
+	}
+	expiry, err := strconv.ParseInt(payload, 10, 64)
+	if err != nil || expiry <= nowMs {
+		return false
+	}
+	want := sessionMAC(key, payload)
+	return subtle.ConstantTimeCompare([]byte(sig), []byte(want)) == 1
+}
+
+// isHTTPS reports whether the browser's connection is encrypted. Behind Traefik
+// the Go server itself speaks plain HTTP, so the forwarded header is the only
+// signal; without this check the Secure cookie would never be set in
+// production, and setting it unconditionally would break http://localhost dev.
+func isHTTPS(r *http.Request) bool {
+	return r.TLS != nil || r.Header.Get("X-Forwarded-Proto") == "https"
+}
+
+func setSessionCookie(w http.ResponseWriter, r *http.Request, key []byte) {
+	http.SetCookie(w, &http.Cookie{
+		Name:     sessionCookieName,
+		Value:    signSession(key, time.Now().Add(sessionTTL).UnixMilli()),
+		Path:     "/",
+		MaxAge:   int(sessionTTL / time.Second),
+		HttpOnly: true,
+		Secure:   isHTTPS(r),
+		SameSite: http.SameSiteLaxMode,
+	})
+}
+
+func clearSessionCookie(w http.ResponseWriter, r *http.Request) {
+	http.SetCookie(w, &http.Cookie{
+		Name:     sessionCookieName,
+		Value:    "",
+		Path:     "/",
+		MaxAge:   -1,
+		HttpOnly: true,
+		Secure:   isHTTPS(r),
+		SameSite: http.SameSiteLaxMode,
+	})
+}