Iphone13 not syncing gmail address with MacBook Air 2020

Connect the Mail app on your iPhone to your email account, using IMAP. Connect an e-mail client on your laptop (Mac or Windows PC) to your email account, using IMAP.

You want IMAP – instead of the other common mail protocol, POP3 – because IMAP leaves your mail in the server (Google's cloud). With POP3 (and a setting to delete the server copy once a device had made a local copy of the mail), some mail might end up only on one device; some mail might end up only on the other.

Google Workspace Admin Help – Set up Gmail with a third-party email client

https://support.google.com/a/answer/9003945?hl=en

gailybuzz Said:

"How to retrieve my email on my iPhone as well as my laptop?"

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Use a New App Password:

Do you use an App Password? If so, try a new App Password. Sometimes, changes (i.e. updates) are made to the device, and then mail server syncing becomes an issue (which is what a new App Password it intended to fix). As an example, go here for gmail: Sign in with App Passwords - Google Account Help - Google

Note that instead of using the iPhone's Mail app with your Gmail account, you could install and use Google's own Gmail app.

https://apps.apple.com/us/app/gmail-email-by-google/id422689480

There's also a Web interface to Gmail that you could access from an iPhone or a laptop in a pinch.