Sounds unusual to me, especially when it’s not working with two independent instances - builder and plugin.
I never faced such issues. All CSS was applied properly - whether I used a plugin (WPCodeBox) or any custom code instance inside the builder.
I would’ve asked you if you set your conditions properly, to display your custom styles on frontend and backend when using a plugin, but since it’s also happening when using the editor’s custom code area(s), I’m not sure what could cause this behavior.
Did you check with the browser tools if the rule is present inside the editor? Maybe it gets overwritten somehow?
Does it happen with other/all custom styles as well?
That’s for frontend only, so it makes sense as it is intended behavior to exclusively apply there.
All custom styles which are applied inside the builder should show up there, as well as styles which are set with a code plugin, provided you set the conditions to frontend and backend (applies only to the plugin).
I might have misunderstood you in first place, as I initially thought you were talking about the custom code areas inside the builder.
Sorry for the confusion.
I’d suggest to use a plugin or child theme, if you want both - apply styles globally and display them inside the builder.
Of course you could also just use a global stylesheet, but sounds for me you want to control things outside of the builder.
Maybe we get some upgrade with the custom code area inside the Cwicly options.
I think they are currently reworked, so maybe we see this at some point.