Dear Windzor89,
Good day! Thank you for posting to Microsoft Community. We are happy to help you.
As per your description, please don’t worry, we can work together to narrow down and resolve the situation.
Based on my test result, it seems that I cannot meet the same behavior as like you described, when I try to embedded SharePoint page into another SharePoint page.
Here are my steps:
I go to SharePoint online site content>Site pages> click the site page and click on "Share" button and copy the share page link and putt the URL link into below iframe to make/create embedded code for SharePoint page.
*<iframe src=***https://support.office.com/en-us/sharepoint"****width="1" height="1"></iframe>
Here is my test screenshot for your reference:


Since you mentioned, "But i got a grey window on top of the web part that will disappear after I hover over it" could you please putt your SharePoint share page URL into above iframe and after create a embedded code insert into Embed webpart of SharePoint online page and verify the result with us.
Also, please try to use In-private browser and use another browser to check if there is any difference.
In the meantime could you please confirm does the problem occur to specific SharePoint online page or all SharePoint pages as well. It will help for us to narrow down your issue.
Your understanding and patience will be highly appreciated. I hope that you are keeping safe and well!
Sincerely,
Waqas Muhammad