I'm super curious about this as well.
A few months ago, I worked on a design system project where we faced this question and decided to focus on CSS only, at least to start. We followed Bulma's example and instructed developers to add classes like is-active or is-loading using a framework of their choice. More complicated functionality will probably require web components or something similar - think data tables, date pickers, etc. - but vanilla CSS isn't a bad place to start.
Here are some examples of what other design systems are doing:
Carbon looks to be experimenting
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