Hi Judith,
If you would like to achieve the requirement with workflow, then please follow steps below:
1. Convert your workflow to real-time workflow(mine has already converted), and make configuration like screenshot below:

2. Add steps: If Speaker:Contact (field) contains data, then update the email field from related contact:


3. Then workflow will works for situations below, the email field will be populated with related contact's email after save the record.
-> When you create a new speaker record.
-> When you change the contact to others.
In my opinion, this method may had a disadvantage: if you remove/clear contact field and save the record,
the email field will be kept with the removed email text and won't be clear.
If you would like to make it perfect, you could add a business rule to clear the field in speaker form editor.(If contact field does not contain data, clear email field)
(Remember to save and publish for both business rule and form)

Unlike the workflow, the br behavior will happen immediately once we remove contact.
Or every functions could be integrated in a javascript function, please let me know if you would like to try code.
Regards,
Clofly