Like all other blocks the CSS class is not applied to the spacer block inside Gutenberg Editor. It is applied on the front-end but not when inside Gutenberg editor.
Confirmed.
Editor:

Frontend:

Related to this I presume, if I register_block_style for core/spacer (I have responsive spacers of different heights), the style is applied on the frontend, but not in the Editor as the class from the style is not added. Would be great to fix. Thanks!
Related to this I presume, if I
register_block_stylefor core/spacer (I have responsive spacers of different heights), the style is applied on the frontend, but not in the Editor as the class from the style is not added. Would be great to fix. Thanks!
Very likely that this is related.
https://github.com/WordPress/gutenberg/pull/23235 should fix all the issues mentioned here.
@oxyc how did you get on with the fix for this?
Most helpful comment
https://github.com/WordPress/gutenberg/pull/23235 should fix all the issues mentioned here.