I created a custom post called Brands. Created all custom fields. Styles the template page using block editor and it shows well. But when I try to edit the wordpress archive page, it does not show block editor. On top of that, archives page does not list of the custom posts.
This generally occurs when you have a plugin installed that is disabling the wordpress gutenburg editor. One of the common plugins that does this is the Classic Editor plugin.
If this plugin isn't installed then Page Builders such as Divi and Avada do have the options to disable the gutenburg editor. Should these not be the cause then you it can also be coming from your theme as themes do have the ability to disable the gutenburg editor.
I would advise checking to see if your plugins/theme is disabling the editor.