Hi there Becks001,
Let's continue by making sure your MacBook Pro is running the latest software version, which is macOS Ventura 13.5.1. You can see the currently installed macOS version by going to the Apple menu () > About This Mac. If needed, learn how to update your Mac here: Update macOS on Mac - Apple Support
Next, your screenshot indicates you aren't seeing any search results at all. If you hit enter on the keyboard after entering text in the search field in Mail, do any results appear?
Also, you mentioned you are able to see these emails on your iPhone; do you have the same email accounts added to Mail on your MacBook Pro? This link provides details about how to view your accounts and get more information: View email account information in Mail on Mac - Apple Support
Additionally, you may want to keep the information below in mind when searching in Mail:
When Mail searches all mailboxes, it searches in the Trash mailbox, but not the Junk mailbox; it doesn’t search encrypted messages, either. To change these options, choose Mail > Settings, click General, then set the options at the bottom of the pane.
Have a look at this support article for more details about how to search in Mail on your Mac: Search for emails in Mail on Mac - Apple Support
Thanks!