Fix API lint errors blocking CI

eslint has been failing on 11 no-explicit-any errors, which kept the
whole pipeline red — including the new publish job that waits on lint.

The casts all worked around missing types rather than unknown shapes:

- jwt: @fastify/jwt decorates the instance at runtime, so the namespace
  is not in FastifyInstance's type. Described the parts we call and cast
  through unknown once, in one place, instead of `as any` at five sites.
- permissions: FastifyInstance.db is declared by the db plugin; the cast
  was stale and hid the real type.
- paginate: the querystring schema already validates page/perPage, so
  the call sites now name that shape via PaginationQuery.

Also dropped an unused import and an unused binding whose call is kept
for its validation side effect.

No behaviour change: eslint and tsc are both clean.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

apps/api/src/plugins/socket.ts

@@ -5,6 +5,7 @@ import { Server as SocketIOServer } from 'socket.io';
 import { nodes, organizationMembers, servers } from '@source/database';
 import { ROLES } from '@source/shared';
 import type { Role } from '@source/shared';
+import { getJwt } from '../lib/jwt.js';
 import type { AccessTokenPayload } from '../lib/jwt.js';
 import {
   daemonOpenConsoleStream,
@@ -67,7 +68,7 @@ export default fp(async (app: FastifyInstance) => {
       return;
     }
 
-    const verifier = (app as any).jwt?.verify;
+    const verifier = getJwt(app)?.verify;
     if (typeof verifier !== 'function') {
       next(new Error('Authentication is not configured'));
       return;