Mints a public share token for a thread. Idempotent: sharing an already-shared thread returns the existing token.
Deletes the share token for a thread. Idempotent: returns 204 whether or not a share token existed. Deliberately does not verify the thread still exists.
Returns the share token for a thread. The token is omitted when the thread is not shared. Gated on runs:share so the control's state matches the control's permission.
