Show a full calendar view for an Event list inside a modern page + allow to "Connect to Outlook"

I want to show a Calendar inside my modern sharepoint online page. Now seems there are 2 ways based on this link https://sharepointmaven.com/how-to-create-a-calendar-view-on-a-sharepoint-list/ ..

1) Create a custom list and use the Calendar view

2) Create an actual Event list

Now I do not want to use the first option as i can not use the "Connect to Outlook" to connect the sharepoint calendar to my outlook on Windows machine, as the source is not an actual event but rather a custom list with a calendar view.

But using the second point, i can use the "Connect to Outlook",

but the problem is that i am unable to show the full calendar view on a modern page in a user friendly way. now i used this Embed web part, with an iframe and IsDlg=1 parameter, as follow:-

but the result i got was not very pleasant, as follow:-

where there is a lot of free space on top + when i click on the "+Add" link to add a new event or click to view existing event >> the event will be shown on the embed web part with all the other screen sections which is not very user friendly, as follow:-

so how i can have a full calendar view inside modern web page in a user friendly and modern way + the ability to use "Connect to Outlook"??

Thanks