fabiotemplate Hello
You're on the right track — the T4 Framework allows you to create multiple profiles for template settings, so you can assign a specific profile to each template style.
In this case, go to Site Settings in the template style assigned to your Home menu item. By default, there are two built-in profiles for this section: default and logistics. You can click the Clone button to create a new profile:

For example, I named the new profile darkMode and set the Dark Mode theme as the default for this profile:

Save this profile, then assign this template style to the menu item(s) where you want Dark Mode enabled by default.
Hope this helps! 😉
Heinz