The short answer
An invitation does not automatically share your personal content. A project must be assigned to the intended team and shared with it. Find this under Switch project → Project properties → Team. The selection may save immediately. Members can use shared projects according to their role, while viewers are intended for read access. General chat and model lists remain user-specific. Seeing a team project therefore does not guarantee access to everyone else's chats and models. Check the content you need separately.