feat(go): scheduled bank sync (Go only)

The Go server now runs sync -> infer -> flush-cache by itself at the
times in SYNC_SCHEDULE (comma-separated HH:MM, default 04:00, "off"
disables), read in SYNC_TZ (default Europe/Prague). Nothing runs at
startup; an invalid value stops the server with an error.

- internal/scheduler: time-of-day parsing, Next, and the run loop
- banksync.Runner: one lock shared by /sync-bank and the scheduler so
  runs never overlap, plus the status of the last run
- footer shows the last sync since start and the next scheduled run
- binary embeds time/tzdata because the Alpine image has no zone data

Deliberately not implemented in the legacy Python app, which is being
phased out; recorded in CLAUDE.md under "Deliberately Go-only features".

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

go/cmd/fuj/main_test.go

@@ -0,0 +1,35 @@
+package main
+
+import (
+	"context"
+	"errors"
+	"fuj-management/go/internal/scheduler"
+	"fuj-management/go/internal/services/banksync"
+	"io"
+	"strings"
+	"testing"
+	"time"
+)
+
+func TestSyncInfo(t *testing.T) {
+	now := time.Date(2026, 10, 8, 12, 0, 0, 0, time.UTC)
+	four := []scheduler.TimeOfDay{{Hour: 4}}
+
+	ok := banksync.NewRunner(func(context.Context, io.Writer) error { return nil })
+	if got := syncInfo(ok, four, time.UTC, now); got != "no sync since start | next 2026-10-09 04:00" {
+		t.Errorf("before any run: %q", got)
+	}
+	if err := ok.Run(context.Background(), "scheduled", io.Discard); err != nil {
+		t.Fatal(err)
+	}
+	got := syncInfo(ok, nil, time.UTC, now)
+	if !strings.HasPrefix(got, "last sync ") || !strings.HasSuffix(got, "(scheduled) ok | scheduled sync off") {
+		t.Errorf("after ok run, schedule off: %q", got)
+	}
+
+	bad := banksync.NewRunner(func(context.Context, io.Writer) error { return errors.New("boom") })
+	_ = bad.Run(context.Background(), "manual", io.Discard)
+	if got := syncInfo(bad, four, time.UTC, now); !strings.Contains(got, "(manual) FAILED | next 2026-10-09 04:00") {
+		t.Errorf("after failed run: %q", got)
+	}
+}