Phase 5 follow-up: discover the \Sent mailbox; record the approved real send (AUD-71)

The approved real test reply was sent and the thread updated (same
X-GM-THRID as the original). The live test exposed one bug: the thread
check hardcoded Gmail's sent mailbox as "[Gmail]/Sent Mail", but this
account exposes it as "[Google Mail]/Sent Mail".

- internal/mailfetch: LIST parser, ListMailboxes, and SentMailbox that
  finds the mailbox flagged \Sent (RFC 6154) with name fallbacks.
- internal/mailops: VerifyThreadUpdated selects the discovered \Sent
  mailbox instead of a hardcoded name.
- cmd/email-agent: -check-thread <id> exercises the check against real
  Gmail without sending mail.
- Tests for LIST parsing, sent-mailbox discovery, and the discovery
  error path.
- docs/phase5-replies.md: record send-as verification, the sent reply's
  thread id, the app confirmation (sent_reply_in_thread=true), and the
  fix.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

internal/mailops/mailops.go

@@ -31,9 +31,6 @@ const (
 	LabelDelete   = "Delete"
 	LabelSaved    = "Saved"
 	repliedPrefix = "Replied-to/"
-	// LabelSent is Gmail's IMAP name for the Sent mailbox. Phase 5 checks it to
-	// confirm a reply joined the original thread.
-	LabelSent = "[Gmail]/Sent Mail"
 )
 
 // ErrNotConfigured means Gmail credentials are missing, so no mailbox action can
@@ -50,6 +47,9 @@ type Conn interface {
 	StoreFlags(uid uint32, op string, flag string) error
 	SearchGmailID(gmailID string) ([]uint32, error)
 	SearchGmailThreadID(threadID string) ([]uint32, error)
+	// SentMailbox returns the server's \Sent mailbox (Gmail may call it
+	// "[Gmail]/Sent Mail" or "[Google Mail]/Sent Mail").
+	SentMailbox() (string, error)
 	Logout() error
 }
 
@@ -164,12 +164,16 @@ func (c *Client) VerifyThreadUpdated(ctx context.Context, threadID string) (bool
 	}
 	defer func() { _ = conn.Logout() }()
 
-	if _, err := conn.Select(LabelSent); err != nil {
-		return false, fmt.Errorf("select %q: %w", LabelSent, err)
+	sent, err := conn.SentMailbox()
+	if err != nil {
+		return false, fmt.Errorf("find the sent mailbox: %w", err)
+	}
+	if _, err := conn.Select(sent); err != nil {
+		return false, fmt.Errorf("select %q: %w", sent, err)
 	}
 	uids, err := conn.SearchGmailThreadID(threadID)
 	if err != nil {
-		return false, fmt.Errorf("search thread %s in %q: %w", threadID, LabelSent, err)
+		return false, fmt.Errorf("search thread %s in %q: %w", threadID, sent, err)
 	}
 	return len(uids) > 0, nil
 }

internal/mailops/mailops_test.go

@@ -21,6 +21,8 @@ type fakeConn struct {
 	searched    []string
 	searchUIDs  []uint32
 	searchErr   error
+	sentMailbox string
+	sentErr     error
 	loggedOut   bool
 }
 
@@ -49,6 +51,15 @@ func (f *fakeConn) SearchGmailThreadID(id string) ([]uint32, error) {
 	f.searched = append(f.searched, "thrid:"+id)
 	return f.searchUIDs, f.searchErr
 }
+func (f *fakeConn) SentMailbox() (string, error) {
+	if f.sentErr != nil {
+		return "", f.sentErr
+	}
+	if f.sentMailbox == "" {
+		return "[Google Mail]/Sent Mail", nil
+	}
+	return f.sentMailbox, nil
+}
 func (f *fakeConn) Logout() error { f.loggedOut = true; return nil }
 
 func configured() *config.Config {

internal/mailops/smtp_test.go

@@ -2,6 +2,7 @@ package mailops
 
 import (
 	"context"
+	"errors"
 	"net"
 	"strings"
 	"testing"
@@ -113,14 +114,34 @@ func TestVerifyThreadUpdatedSearchesSentMailbox(t *testing.T) {
 	if !ok {
 		t.Error("VerifyThreadUpdated() = false, want true when the thread has a sent message")
 	}
-	if fc.selected != LabelSent {
-		t.Errorf("selected = %q, want %q", fc.selected, LabelSent)
+	if fc.selected != "[Google Mail]/Sent Mail" {
+		t.Errorf("selected = %q, want the discovered sent mailbox", fc.selected)
 	}
 	if len(fc.searched) != 1 || fc.searched[0] != "thrid:987654321" {
 		t.Errorf("searched = %v, want [thrid:987654321]", fc.searched)
 	}
 }
 
+func TestVerifyThreadUpdatedUsesDiscoveredSentMailbox(t *testing.T) {
+	fc := &fakeConn{uidValidity: 3, searchUIDs: []uint32{5}, sentMailbox: "[Gmail]/Sent Mail"}
+	c := newFakeClient(fc)
+	ok, err := c.VerifyThreadUpdated(context.Background(), "77")
+	if err != nil || !ok {
+		t.Fatalf("VerifyThreadUpdated() ok=%v err=%v", ok, err)
+	}
+	if fc.selected != "[Gmail]/Sent Mail" {
+		t.Errorf("selected = %q, want the configured sent mailbox", fc.selected)
+	}
+}
+
+func TestVerifyThreadUpdatedSentMailboxError(t *testing.T) {
+	fc := &fakeConn{sentErr: errors.New("no sent mailbox")}
+	c := newFakeClient(fc)
+	if _, err := c.VerifyThreadUpdated(context.Background(), "77"); err == nil {
+		t.Fatal("VerifyThreadUpdated() error = nil, want a sent-mailbox discovery error")
+	}
+}
+
 func TestVerifyThreadUpdatedEmptyThread(t *testing.T) {
 	c := newFakeClient(&fakeConn{searchUIDs: nil})
 	if _, err := c.VerifyThreadUpdated(context.Background(), ""); err == nil {