What problems was I solving

The management-ui API barrel re-exported seven symbols from @architect/management-ui-view-model, but all production call-sites had already moved to the view-model directly in earlier refactors (#3447, #3481). Leaving the re-exports in place created unnecessary public surface and barrel indirection.

What user-facing changes did I ship

None. This is a behind-the-scenes cleanup with no visible UI, auth, routing, or behavioral changes.

How I implemented it

Removed the unused re-exports from architect/management-ui/app/main/api/api.tsx and architect/management-ui/app/main/api/session-api.ts while keeping the internal imports required by ApiProvider and useGuestAuthenticationState. A full repo grep confirmed no remaining consumers of any of the removed symbols.

Description for the changelog

Removed seven unused re-exports from the management-ui API barrel, including api, createManagementQueryClient, createManagementTrpcClient, managementQueryClient, managementTrpcClient, getGuestAuthenticationState, and GuestAuthenticationState, since all production consumers had already shifted to @architect/management-ui-view-model.