If the Clerk as an email admin has access to the full archive then the Clerk can do this, otherwise, it falls to councillors to collate and provide to the Clerk.
If you have used your personal email addresses for council business then those emails are also subject to FOI, including if you have wrote an email about email the councillor (e.g. as an insult between two councillors about the FOI requester) as also subject to FOI.
If the request has asked for ALL data held then it includes your emails.
(My Day Job is FOI and GDPR)