Provider availability was derived independently in the chat picker, the
settings page and the automation hook, mixing provider types with account
ids, so the same provider could look available or unavailable depending on
which response arrived last.

The gateway is now the single source of truth: every provider it returns
carries the nodeId/nodeName of the device it runs on, and clients apply one
scoping rule — a project pinned to a device sees that device's providers
plus Jait; on the gateway everything is listed, labelled by device.

- route model requests by the provider account's own device instead of the
  caller-supplied nodeId, which 404'd whenever the open project's device
  disagreed with the selected provider
- key ACP fallback models by provider type, not account id, and never cache
  an empty list — this pinned account pickers to "no models" until restart
- share one /api/providers request through a provider store instead of four
  independent fetches and caches
- allow login for device-hosted accounts from the chat picker
- drop the unused provider-selector component

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