Why a new contact isn't in the Speakers view

Speakers under CRM is not a separate list you add people to. It is All Contacts filtered to people who are attached to at least one session as a speaker — the same way Chairpersons and Moderators are filtered to those roles.

Creating a contact is step one: they now exist in All Contacts. To make them a speaker, open a session and add them as a participant with the Speaker role. The moment they are on a session they appear in Speakers, and the Session - Accepted, Pending and Declined tabs at the top of that view sort them by the status of the sessions they are on.

A contact who is only a submitter, an additional contact or a portal user with no session stays in All Contacts and their own view. See create a session for adding participants, and filter contacts by role or session status for the tabs.