Finally got a feedback from Squarespace support:
So contrary to common belief the 7.1 templates are not all the same at core. If you start with a dark template you will get a dark layout for the core / default pages of your site such as cart, 404 page, templates displayed by default, etc...
The workaround is to edit the dark color theme to the one you wish as default (so yeah no I have a light theme named "dark", so confusing...)
Very frustrating.
