paging: paging groups, *80 intercom, auto-answer headers

/api/paging-groups CRUD (members as memberIds). The generator renders
sp-page-{id} per 03 §6.11 (desk phones only, auto-answer headers via
sp-sub-autoanswer) plus the number in sp-local-numbers. Added the `s`
option so phones already on a call aren't paged, which also keeps a
pager who is a member from being paged themselves. A group with no
members just hangs up.

*80<ext> intercom checks the target first: digits only and an endpoint
in sp-from-ext, else ss-noservice (the spec's one-liner passed
${EXTEN:3} straight into Page()). Both written back into 03.

Web: Paging page (list, drawer form with member checkboxes). Golden
case paging. e2e m8-t4 with baresip phones that honor the headers
(sip_autoanswer): an ordinary call rings, a page is answered by itself
and muted, the busy pager is skipped, *80 is two-way, *80999 refused.
The check on a real Yealink/Grandstream stays open (09).

Task: M8-T4

apps/api/src/generator/load.ts

@@ -10,6 +10,8 @@ import {
   extensions,
   holidays,
   ivrOptions,
+  pagingGroupMembers,
+  pagingGroups,
   ivrs,
   outboundRoutes,
   queueMembers,
@@ -126,6 +128,15 @@ export type SnapConference = {
   record: boolean;
 };
 
+export type SnapPagingGroup = {
+  id: string;
+  number: string;
+  name: string;
+  duplex: boolean;
+  /** Extension numbers. */
+  members: string[];
+};
+
 export type SnapIvr = {
   id: string;
   number: string;
@@ -179,6 +190,7 @@ export type Snapshot = {
   ringGroups: SnapRingGroup[];
   queues: SnapQueue[];
   conferences: SnapConference[];
+  pagingGroups: SnapPagingGroup[];
   ivrs: SnapIvr[];
   timeConditions: SnapTimeCondition[];
   holidays: SnapHoliday[];
@@ -233,6 +245,11 @@ export async function loadSnapshot(db: Db, now = new Date()): Promise<Snapshot>
     .from(queueMembers)
     .innerJoin(extensions, eq(extensions.id, queueMembers.extensionId));
   const confRows = await db.select().from(conferences);
+  const pageRows = await db.select().from(pagingGroups);
+  const pagedRows = await db
+    .select({ groupId: pagingGroupMembers.pagingGroupId, number: extensions.number })
+    .from(pagingGroupMembers)
+    .innerJoin(extensions, eq(extensions.id, pagingGroupMembers.extensionId));
   const ivrRows = await db.select().from(ivrs);
   const tcRows = await db.select().from(timeConditions);
   const holidayRows = await db.select().from(holidays);
@@ -335,6 +352,13 @@ export async function loadSnapshot(db: Db, now = new Date()): Promise<Snapshot>
       maxMembers: c.maxMembers,
       record: c.record,
     })),
+    pagingGroups: pageRows.map((g) => ({
+      id: g.id,
+      number: g.number,
+      name: g.name,
+      duplex: g.duplex,
+      members: pagedRows.filter((m) => m.groupId === g.id).map((m) => m.number),
+    })),
     routes: routeRows.map((r) => ({
       id: r.id,
       name: r.name,