In my experience it varies a lot. Even in our own system certain emails are stored differently. There are a few "we legally have to deliver this email and might need to prove it later" notifications. We store a PDF of those in s3. For others we might just save the data, a sent timestamp, and a key for which email visual template was used.

I also thought of a counter argument to my point overnight. We don't store one super duper high volume email which is the email that only has an MFA code. We would also absolutely never ever dream about allowing a plaintext password in an email, so we're probably following different patterns in the first place.