1.To make users in the Group A can upload or modify site assets (.mp4, jpg, pdf), you should go to site contents -> site assets -> library settings -> permissions for this document library -> grant Group A edit permission.
2.Based on your description, I understand that you want to only Group A can edit pages. And others can view pages in the browser. Go to site contents -> site pages -> library settings -> permissions for this document library -> grant Group A edit permission and make others read permission.
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