Surfaces the federatedRegistrationOpen flag (Task 1 schema column) on the
admin settings GET/PATCH endpoints and the public /api/instance/info
endpoint. Closes the 3 deferred TypeScript errors from Task 2 by
populating the now-required InstanceAdminSettings/InstanceInfoResponse
field.
Adds smoke tests (routes/instance.test.ts, routes/settings.test.ts) that
lock in the JSON contract the Connections UI (Task 21) and admin
RegistrationPanel (Task 15) consume, plus boolean-validation coverage
for the PATCH path. Updates docs/systems/admin.md with the new field in
both InstanceAdminSettings and the public info response schema.