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/routes/auth/index.ts

@@ -3,7 +3,7 @@ import { eq } from 'drizzle-orm';
 import { users } from '@source/database';
 import { hashPassword, verifyPassword } from '../../lib/password.js';
 import { signAccessToken, signRefreshToken, verifyRefreshToken } from '../../lib/jwt.js';
-import type { AccessTokenPayload, RefreshTokenPayload } from '../../lib/jwt.js';
+import type { RefreshTokenPayload } from '../../lib/jwt.js';
 import { AppError } from '../../lib/errors.js';
 import { RegisterSchema, LoginSchema } from './schemas.js';