How to make modifiers for the wrapper block?

Question

css

If I understand correctly that if there is some kind of background around the block (and even more so, this block has a width limit and a centerer), then this background should be separated into a separate block. But tell me how to choose the right modifiers for the wrapper block? It's just that if the background is gray, you can write block-wrap--grey, but if the image? By image content? And most importantly, each such block on the page has different margins at the top and bottom. It's useless to fight with the designer and the only option is to use the atomic css approach? Like block-wrap--pd-t-50? Who does what? Or even make the wrapper itself part of the block, what's inside?