Dear Erica Newman
Thank you for using Microsoft products and visiting the community!
I think you have a misconception about classic outlook and new outlook.
The switch between classic outlook and new outlook is the switch of the configured mailboxes at that time, that is to say, you configure 1 gmail mailbox on classic outlook, and then you configure 3 gmail mailboxes on new outlook, when you switch, there will not be the other 2 gmail mailboxes newly configured on classic outlook.
While new outlook is based on web development, classic outlook is based on system development, so compared to compatibility and functional stability, classic outlook is much better than new outlook.
I can understand that you don't want to use classic outlook, the screen of new outlook is better than that of classic outlook, for you you tend to keep using new outlook, but my suggestion is that you still use classic outlook.
You can try to configure your gmail mailbox on classic outlook and wait for the synchronized mail.
Regarding the calendar issue, you configured your gmail mailbox and the protocol configured on outlook, if it is the imap protocol, by the nature of this protocol, it is not possible to synchronize, including contacts.
You asked if you can use an older version, if you configured the IMAP protocol, you can try uninstalling the older version and installing the version you mentioned. It will synchronize the emails.
Below is the outlook for mac history version record, you can find the version you want to download download.
Update history for Office for Mac - Office release notes | Microsoft Learn
Best wishes
Clark | Microsoft Community Support Specialist