Attaches an existing organisation to an existing game. The game's owner organisation performs the attach: the caller must be an administrator of the owner organisation and must act as it, so an x-org-id naming a linked organisation other than the owner is refused with 403. The target organisation must exist and must not be soft-deleted (404), and must not already be linked to the game (409). The link is what gives another organisation's members access to the game: users.CanWorkWithGame, the admin game scope, the publisher dashboard and insights all read it. Attaching does not change games.owner_organisation_id, so the owner keeps the game's identity attribution and the owner-only routes.