Ok so I think I finally found a way to do what I was looking for.
I added these lines in the dotspacemacs/user-config block in my ~/.spacemacs config:
(define-key evil-motion-state-map (kbd "S-<up>") 'evil-scroll-page-up)
(define-key evil-motion-state-map (kbd "S-<down>") 'evil-scroll-page-down)
Not sure if that’s the recommended way but it seems to work
