saving mail in mail application

Hello FECFRN.

Welcome to Apple Support Communities. We understand that you want to save your messages in the Mail app on your Mac. We’re happy to help.

Please use the steps her to archive your emails that you want to keep: Archive emails in Mail on Mac - Apple Support

Emails that you archive won’t delete until you delete them.

Let us know if you have further questions.

Take care.

See the article Move or copy emails in Mail on Mac - Apple Support

You can move mail messages in a folder created on my Mac section , the iCloud inbox having 16 k mails will get empty , however the new mails will still arrive in iCloud mail inbox .

Archiving of mails is automatic in imap gmail account , if the mails are in iCloud the second method as suggested in thread can also be followed .

Hey FECFRN,

One tip I got from a Mac specialist was to create a Smart Mailbox titled Today. That way I can process all the mail from today and then keep going through the older emails. I also created Smart Mailboxes for things like Amazon that has been a constant in my Inbox in 2020. Good Luck!