Based on your description, I understand that you want to show personal outlook calendar events in the communication site home page.
There is no OOTB web part to show personal outlook calendar in the communication site home page. As a workaround, you could use Power Automate to pull all personal outlook calendar events into a SharePoint list. Then create a calendar view in the SharePoint list. At last insert the SharePoint list into communication site home page, choose the calendar view.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.