fix(server): honor periodic_interval_days for Immich periodic summary

The APScheduler cron job fires daily at every entry in `periodic_times`,
and nothing in the dispatch path consulted `periodic_interval_days` or
`periodic_start_date` — so a configured 3-day interval still produced a
daily summary.

Gate the dispatch in `dispatch_scheduled_for_tracker` for kind=periodic
via `(today_in_app_tz - start_date).days % interval == 0`. Log a skip
with reason `interval_not_due` on non-firing days so operators can tell
suppressed-by-interval apart from other skip causes.

packages/server/src/notify_bridge_server/services/scheduled_dispatch.py

@@ -22,7 +22,9 @@ the test-dispatch path in ``manual_dispatch``.
 from __future__ import annotations
 
 import logging
+from datetime import datetime
 from typing import Literal
+from zoneinfo import ZoneInfo, ZoneInfoNotFoundError
 
 from sqlmodel import select
 from sqlmodel.ext.asyncio.session import AsyncSession
@@ -64,6 +66,43 @@ _SKIP_REASON_NO_LINKS = "no_enabled_links"
 _SKIP_REASON_NO_EVENT = "provider_returned_no_event"
 _SKIP_REASON_EMPTY_PAYLOAD = "zero_assets_matched"
 _SKIP_REASON_NO_TARGETS = "no_targets_after_filtering"
+_SKIP_REASON_INTERVAL_NOT_DUE = "interval_not_due"
+
+
+def _periodic_due_today(default_tc: TrackingConfig, app_tz: str) -> bool:
+    """Return True iff today (in app tz) falls on the periodic schedule.
+
+    The schedule is ``start_date + N * interval_days`` for non-negative N.
+    The cron job fires every day at the configured ``periodic_times`` — this
+    gate skips the dispatch on days that aren't a multiple of the interval
+    from the start date, so a user-configured ``interval_days=3`` fires every
+    third day rather than every day.
+
+    Defensive: an interval ≤ 1 is treated as "fire daily"; an unparseable
+    ``periodic_start_date`` is treated as "fire" so a bad config doesn't
+    silently stop all summaries (operators see notifications and can fix it).
+    """
+    interval = max(1, int(getattr(default_tc, "periodic_interval_days", 1) or 1))
+    if interval <= 1:
+        return True
+    raw_start = getattr(default_tc, "periodic_start_date", "") or ""
+    try:
+        start = datetime.strptime(raw_start, "%Y-%m-%d").date()
+    except (ValueError, TypeError):
+        _LOGGER.warning(
+            "Invalid periodic_start_date %r; treating periodic as due today",
+            raw_start,
+        )
+        return True
+    try:
+        tz = ZoneInfo(app_tz)
+    except (ZoneInfoNotFoundError, ValueError):
+        tz = ZoneInfo("UTC")
+    today = datetime.now(tz).date()
+    delta_days = (today - start).days
+    if delta_days < 0:
+        return False
+    return delta_days % interval == 0
 
 
 async def _log_skip(
@@ -181,6 +220,28 @@ async def dispatch_scheduled_for_tracker(
         collection_ids = list(tracker.collection_ids or [])
 
         app_tz = await get_app_timezone(session)
+
+        # Periodic summary respects an N-day interval starting from
+        # ``periodic_start_date`` — the cron job fires every day at
+        # ``periodic_times``, so without this gate a configured
+        # ``interval_days=3`` would still dispatch daily. Other kinds
+        # (scheduled/memory) don't have an interval setting.
+        if kind == "periodic" and not _periodic_due_today(default_tc, app_tz):
+            _LOGGER.info(
+                "Periodic for tracker %d: not due today (interval=%s, start=%s)",
+                tracker_id,
+                getattr(default_tc, "periodic_interval_days", None),
+                getattr(default_tc, "periodic_start_date", None),
+            )
+            await _log_skip(
+                tracker_id, kind, _SKIP_REASON_INTERVAL_NOT_DUE,
+                tracker_user_id=tracker.user_id,
+                tracker_name=tracker.name or "",
+                provider_id=provider.id,
+                provider_name=provider.name or provider.type,
+            )
+            return
+
         link_data = await load_link_data(session, tracker_id)
 
     if not link_data: