feat(#259): id-based reconcile for schedule-items replace (backend + DTO)

Add optional `int? Id` to ScheduleItemRequest/ReplaceProgramScheduleItem so
a client can round-trip each existing item's server id. When ids are present,
ReplaceProgramScheduleItemsHandler reconciles by id (not array position), so an
item's persisted fill-group/shuffle state (PlayoutScheduleItemFillGroupIndex,
FK OnDelete Cascade) follows the logical item across reorders/inserts instead of
being inherited by whatever previously occupied its new slot (#259, split from
#252/#253). A fully id-less payload keeps the verbatim positional fallback.

Guards (inside PersistItems, after CheckVersion so 412 precedes 422): duplicate
id -> 422; id not in this schedule -> 422 (a stale id under Phase-1 force-write is
a live lost-update signal, not a new item). Index stays array-position derived.

Regenerated v1.json + TS client.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

ErsatzTV/Controllers/Api/Requests/ScheduleItemRequest.cs

@@ -4,7 +4,14 @@ using ErsatzTV.Core.Scheduling;
 
 namespace ErsatzTV.Controllers.Api.Requests;
 
+/// <param name="Id">
+/// Server-assigned identity of an existing schedule item, as returned by GET /api/schedules/{id}/items.
+/// Omit (or send null / 0) for a new item. On a replace, the item carrying this id keeps its persisted
+/// fill-group/shuffle progression even when moved to a different position. Unknown or duplicated ids are
+/// rejected with 422 — never fabricate an id.
+/// </param>
 public record ScheduleItemRequest(
+    int? Id,
     StartType StartType,
     TimeSpan? StartTime,
     FixedStartTimeBehavior? FixedStartTimeBehavior,
@@ -86,6 +93,9 @@ public record ScheduleItemRequest(
 
     public ReplaceProgramScheduleItem ToReplaceCommand(int index) =>
         new(
+            // normalize the two-state client value (null / 0 / positive) to the handler's null-or-real
+            // contract so 0-defaulting clients read as "new item" rather than "existing item 0"
+            Id is > 0 ? Id : null,
             index,
             StartType,
             StartTime,