How to recover old emails

I purchased a new IMac desktop because my other one was really slow with too many pictures and videos. I thought I saved all my emails but didn't. Is there a way to get all my old emails back? Thanks!

Your emails are retained on the provider's servers provided you haven't deleted them, moved them offline somewhere, or if their retention policies remove emails after some period of time. When you log into your iCloud email, any messages that you have kept are displayed. Messages moved to trash are deleted after 30 days by default.

Any email that you have will display in your email accounts.

But that's the problem. It is NOT displaying in my iCloud accounts.

Same problem. It's Not displaying in my iCloud accounts