Your are mixing CSS declaration and YAML. If you use card-mod-card: then the entry needs to be CSS string (can be multiline). If you want to use yaml then use card-mod-card-yaml
So (untested) your theme entry should be more like
generic:
card-mod-theme: generic
card-mod-card-yaml: |
round-slider$: |
.slider {
stroke-width: 15px !important;
--round-slider-path-color: slategrey !important;
}