Are gutenberg blocks ideally supposed to look the same in both back-end and front-end?

Ideally, yes. Blocks are supposed to be WYSIWYG. See the Editor Styles section of the Gutenberg Handbook for how to load theme styles in the editor.

You need to add an editor stylesheet with add_editor_style(), the same way you did with the previous editor, but to support the block editor you need to declare theme support for editor styles:

add_theme_support( 'editor-styles' );