Hello MisterLester,
Thank you for using Apple Support Communities!
We understand from your post that you are only receiving your Gmail emails in the evenings and then they all disappear from your inbox until the next evening. Does this also happen when you sign in to your Gmail account from a web browser? If so, that would indicate that there is a setting within the Gmail account that is causing the issue. As you have removed the accounts and added them again to your devices, but still encounter the issue, that too, would indicate that it is something within the Google settings causing the issue.
A few things to check on your Mac, would be to see if there are any rules set up. This article will provide you with information on using rules to manage your emails so you can see if any of them are affecting your Gmail:
Use rules to manage emails you receive in Mail on Mac - Apple Support
Also, check the Do Not Disturb settings on your Mac and other devices to see if it is enabled and has a schedule set.
Use notifications on your Mac - Apple Support
Let us know how it goes.
Best Regards.