How to link back to the original site the user came from after he jumped to a subdomain with a "different" product?

lets say you have a site called "example.com", which is the homepage of a company that provides a login for its customers and different functions like a personal backoffice, learning material and company related stuff like news, about etc.

One of the things that site contains is a link to a sub-domain which basically is a media-area for the customers where they can watch videos from different topics that are related to their daily work, when the user clicks on that link, the sub-domain (lets call it videos.example.com) opens in a new tab.

What the project manager suggested

He wanted to add a home-icon next to the company logo on the left of the head-area, the company logo should act as a link to "example.com" the home icon should link back to "videos.example.com".

In my opinion thats to confusing for the user, since we are currently using a home-icon on "example.com" as a link back to the starting-page, users might expect that the home-icon will take them back to "example.com" instead of "videos.example.com", also most users click on the logo to jump back to the starting page, which makes it even more confusing.

I said we should not place them next to each other, we should only use the logo instead of a home-icon to take the user back to the starting page.

I still want to provide the users a way to get "back" to "example.com", and now i am looking for a good, understandable way how to do this.

Do you have any proposals on how to make that as transparent as possible?

Btw. the header will consist of Logo + 5 navigation points + search bar + login option