Having a choice selection pop up right after main navigation use

I am working on a web-based application (only desktop) where users could enter new sets of data to the system by using preformed templates. As this is one of the main actions in the system, we will have a New Data Entry button on the main navigation which works like a drawer menu; when sth from the menu is clicked, the menu collapses.

As users need to select a template to go to the New Data Entry screen, when a user clicks New Data Entry from the drawer menu, I want to first make them select a template from the list and I do it with a pop up. (We use the same pop up if users want to change the template later while entering new data.)

But I find it a bit weird to show a pop up right after making an action on the main navigation. I would like to use a full-screen pop-up, at least in that way I wouldn't see the recently used drawer and whatever I was on before under the overlay and it would be more focused, but we don't use full-screen pop-ups anywhere on the system so I need to suggest a smaller pop up with an overlay behind.

Do you have any idea on showing a pop up right after clicking a menu item? Do you also think it is a bit odd? If I use it, should it appear over the last screen I was on (whatever it is), or should it appear on New Data Entry screen; where the user will land on after selecting a template? (My idea is the first one, as if the user closes this pop up without selecting a template, they should land on where there were before.)

Could you think of any similar experiences I could try and see how they applied it?

Thanks!