Hi Bill H :-)
Re: "Gmail account offline on Apple Mail" : " ... will not let me activate it as "online" anymore."
You might want to log-in to your GMail account online, and see if there's something that needs your attention
Eg: If emails are not set to delete after downloading, you may have reached Gmail's limit of storage for emails,
or various possibilities: Gmail may have made changes that are affecting delivery to Apple's "Mail" app
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Re: "I am afraid to delete the Account and recreate it because I am afraid I can lose all of my messages"
Depending on your email organization methods, and settings:
✽ Your email messages may be saved "On your Mac" or even still be stored on the Gmail server
✽ From the Mail app: email mailboxes (folders) can be exported and imported if you want
You may be backing up data to an external drive (eg: using Time Machine) for safe=keeping / retrieval
For MacOS Ventura: Mail User Guide for Mac - Apple Support
✽ For access to all the "How-to" methods / articles:
You can click "Table of contents" at the top of the "welcome" page that opens from the link above
All the best :-)