Try adding iframe code like this:
You can find full embed code at: Add Modern Calendar to a SharePoint Online page
To hide navigation & see the calendar in full ...
Event web part is the OOB web part in SharePoint Online and we could not change it.
In short, we cannot automatically update the From and To dates in the date range, and must manually change it.
Or you’ll have to look into a custom event spfx webpart, specify this month date range and install it.