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

packages/shared/src/index.ts

@@ -15,6 +15,7 @@ export * from './sounds.ts';
 export * from './ringgroups.ts';
 export * from './queues.ts';
 export * from './conferences.ts';
+export * from './paging.ts';
 export * from './ivrs.ts';
 export * from './timeconditions.ts';
 export * from './announcements.ts';

packages/shared/src/paging.ts

@@ -0,0 +1,27 @@
+// SPDX-License-Identifier: AGPL-3.0-or-later
+// Paging groups (02 paging_groups, 03 §6.11): a number that makes several desk phones answer by
+// themselves and play what the caller says.
+import { z } from 'zod';
+import { InternalNumber } from './extensions.ts';
+
+const PagingGroupFields = z.object({
+  number: InternalNumber,
+  name: z.string().trim().min(1, 'Required').max(40),
+  /** false: one-way announcement; true: intercom, the paged phones can talk back. */
+  duplex: z.boolean(),
+  /** Extension ids. */
+  memberIds: z
+    .array(z.uuid())
+    .max(50)
+    .refine((ids) => new Set(ids).size === ids.length, 'Someone is listed twice'),
+});
+
+export const PagingGroupCreateSchema = PagingGroupFields.partial().required({
+  number: true,
+  name: true,
+});
+export const PagingGroupUpdateSchema = PagingGroupFields.partial();
+export type PagingGroupCreate = z.input<typeof PagingGroupCreateSchema>;
+export type PagingGroupUpdate = z.input<typeof PagingGroupUpdateSchema>;
+
+export type PagingGroupDto = z.output<typeof PagingGroupFields> & { id: string; createdAt: string };