Get Client Intake Form

Retrieves an intake form on behalf of the client who is filling it out.

Returns the client-facing projection (ClientIntakeForm), which omits partner-only data such as clientEmails, teamMemberIds, and sourceMaterials.

Access is client-based, not account-based: the logged-in caller's email address must match one of the form's clientEmails. A form that hasn't been shared (empty clientEmails) authorizes no client. The call fails with PERMISSION_DENIED if the caller's email isn't listed, and with FAILED_PRECONDITION if the caller's identity has no email address.

context is returned only when CONTEXT is included in fields.