Deleting a connection in one browser left the same connection stuck in
every other browser/tab. The user could not delete or edit it from there
because the local state never caught up with the server, and clicks
either no-op'd or threw on a missing-row backend response.
Two pieces caused the bug:
1. `ChatProvidersSettings` ran its backend sync once on mount and then
silently kept localStorage providers whenever `listProviderConfigs`
returned an empty array, on the assumption that an empty server
response had to be a transient glitch. That assumption is wrong when
another browser removed the last connection. With the guard gone,
trust any successful API response, including an empty list. A focus /
visibilitychange listener now triggers a silent re-sync so the dialog
does not need to be closed and reopened to pick up remote deletes.
2. `deleteProviderConfig` threw on HTTP 404, so once Browser A deleted a
connection, Browser B's "Delete" click failed and the local row stuck
around. Treat 404 as success: the server's job is already done and
the local cache only needs to be pruned.
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