fix(email): warmer onboarding copy + Reply-To/Date headers

Personalize the access-request and approval emails, add a real Date header and a
Reply-To (approval -> admin, new-request -> requester) so they read as a
conversation rather than a no-reply blast — small nudges for deliverability;
sender reputation still does most of the work.

backend/app/email.py

@@ -8,6 +8,7 @@ import logging
 import smtplib
 import ssl
 from email.message import EmailMessage
+from email.utils import formatdate
 
 from app.config import settings
 
@@ -18,7 +19,11 @@ def email_enabled() -> bool:
     return bool(settings.smtp_host and settings.smtp_user and settings.smtp_password)
 
 
-def _send(to: list[str], subject: str, body: str) -> bool:
+def _admin_contact() -> str | None:
+    return next(iter(sorted(settings.admin_email_set)), None)
+
+
+def _send(to: list[str], subject: str, body: str, reply_to: str | None = None) -> bool:
     recipients = [e for e in to if e]
     if not recipients:
         return False
@@ -29,6 +34,11 @@ def _send(to: list[str], subject: str, body: str) -> bool:
     msg["Subject"] = subject
     msg["From"] = settings.smtp_from or settings.smtp_user
     msg["To"] = ", ".join(recipients)
+    # A real Date and a Reply-To (so it's a conversation, not a no-reply blast) both
+    # nudge spam filters the right way; reputation still does most of the work.
+    msg["Date"] = formatdate(localtime=True)
+    if reply_to:
+        msg["Reply-To"] = reply_to
     msg.set_content(body)
     try:
         with smtplib.SMTP(settings.smtp_host, settings.smtp_port, timeout=20) as s:
@@ -43,18 +53,23 @@ def _send(to: list[str], subject: str, body: str) -> bool:
 
 
 def send_access_approved(email: str) -> bool:
-    return _send(
+    admin = _admin_contact()
-        [email],
+    body = (
-        "Your Subfeed access is approved",
+        "Hi,\n\n"
-        "Good news — your access to Subfeed has been approved.\n\n"
+        "Your request to use Subfeed has been approved — welcome aboard.\n\n"
-        "Sign in with this Google account to start browsing your subscriptions.\n",
+        "Just open Subfeed and sign in with this Google account, and your YouTube\n"
+        "subscriptions feed will be ready.\n\n"
+        "If you weren't expecting this, you can ignore the message.\n\n"
+        "— Subfeed"
+        + (f"\n\nQuestions? Just reply to this email ({admin})." if admin else "")
     )
+    return _send([email], "You're in — your Subfeed access is approved", body, reply_to=admin)
 
 
 def send_admin_new_request(admins: list[str], requester: str) -> bool:
-    return _send(
+    body = (
-        admins,
+        f"{requester} just requested access to Subfeed.\n\n"
-        "Subfeed: new access request",
+        "Open Subfeed → Settings → Account → Access requests to approve or deny it.\n\n"
-        f"{requester} has requested access to Subfeed.\n\n"
+        "(Reply to this email to reach the requester directly.)\n"
-        "Approve or deny it in Settings → Admin.\n",
     )
+    return _send(admins, f"Subfeed access request from {requester}", body, reply_to=requester)