feat: make Django configs drive backups and scheduling

Treat SQL-backed Django models as the source of truth for pobsync
configuration, exporting runtime YAML only as a compatibility layer for
the existing engine. Add a database-driven scheduler command, Docker
scheduler services, schedule run-state fields, and tests for scheduler,
config export, and retention behavior.

src/pobsync_backend/scheduler.py

@@ -0,0 +1,88 @@
+from __future__ import annotations
+
+from dataclasses import dataclass
+from datetime import datetime
+
+
+@dataclass(frozen=True)
+class CronSchedule:
+    minute: str
+    hour: str
+    day_of_month: str
+    month: str
+    day_of_week: str
+
+
+def parse_cron_expr(expr: str) -> CronSchedule:
+    parts = expr.strip().split()
+    if len(parts) != 5:
+        raise ValueError("cron expression must have exactly 5 fields")
+    return CronSchedule(*parts)
+
+
+def due_key(moment: datetime) -> str:
+    return moment.strftime("%Y%m%d%H%M")
+
+
+def is_due(expr: str, moment: datetime) -> bool:
+    schedule = parse_cron_expr(expr)
+    cron_dow = (moment.weekday() + 1) % 7
+    return (
+        _field_matches(schedule.minute, moment.minute, 0, 59)
+        and _field_matches(schedule.hour, moment.hour, 0, 23)
+        and _field_matches(schedule.day_of_month, moment.day, 1, 31)
+        and _field_matches(schedule.month, moment.month, 1, 12)
+        and _field_matches(schedule.day_of_week, cron_dow, 0, 7, sunday_alias=True)
+    )
+
+
+def _field_matches(field: str, value: int, min_value: int, max_value: int, sunday_alias: bool = False) -> bool:
+    for part in field.split(","):
+        if _part_matches(part.strip(), value, min_value, max_value, sunday_alias=sunday_alias):
+            return True
+    return False
+
+
+def _part_matches(part: str, value: int, min_value: int, max_value: int, sunday_alias: bool) -> bool:
+    if not part:
+        return False
+
+    step = 1
+    base = part
+    if "/" in part:
+        base, step_s = part.split("/", 1)
+        if not step_s.isdigit():
+            return False
+        step = int(step_s)
+        if step <= 0:
+            return False
+
+    if base == "*":
+        start = min_value
+        end = max_value
+    elif "-" in base:
+        start_s, end_s = base.split("-", 1)
+        if not start_s.isdigit() or not end_s.isdigit():
+            return False
+        start = int(start_s)
+        end = int(end_s)
+    elif base.isdigit():
+        start = end = int(base)
+    else:
+        return False
+
+    values = _normalize_values(range(start, end + 1), sunday_alias=sunday_alias)
+    normalized_value = 0 if sunday_alias and value == 7 else value
+    if normalized_value not in values:
+        return False
+    return (normalized_value - min(values)) % step == 0
+
+
+def _normalize_values(values: range, sunday_alias: bool) -> set[int]:
+    out: set[int] = set()
+    for value in values:
+        if sunday_alias and value == 7:
+            out.add(0)
+        else:
+            out.add(value)
+    return out