Include Block Variation Within InnerBlocks

Block variations are not block types, you need to add a group block, and give it the necessary attributes.

As for what those attributes are, you’re the one who chose them when you registered the block, and it looks like there’s even a function that checks for it:

        attributes: { 
            tagName: 'dialog',
            className: 'carousel-modal',
            namespace: 'st/core-group-dialogmodal'
...
        isActive: ({namespace, query}) => {
            return (
                namespace === 'st/core-group-dialogmodal'
            )
        }

So specify the namespace attribute:

['core/group', { namespace: 'st/core-group-dialogmodal' } ],

Keep in mind though that the code in the question will result in 2 nested group blocks, it might have been better to create a carousel group block, then used its class names to style any direct dependents as slides. This way you could put a query block inside the carousel, or manually insert items, and they could be standard group blocks, not variations.

Importantly, instead of relying on .carousel-modal to style each slide in the carousel you would use the > selector e.g. .carousel > * would select any direct immediate descendents. This avoids all the problems with group blocks having controls that would mess up your styling, or being able to insert group blocks that don’t fit your design, or how to add additional slides manually to the start or end of the carousel