Gutenberg Blocks: how to determine an index of the current inner block?

I’m trying to implement a bootstrap5 carousel component as a Gutenberg block. It all appears to be working as intended, except for adding the "active" class to a first element.

I tried to find siblings of the current inner block by using getBlockParents and getBlocksByClientId
Here is the JS code:

    const select = window.wp.data.select('core/block-editor');

    blocks.registerBlockType('natural/bootstrap5-carousel-item', {
        apiVersion: 2,
        title: __('Carousel Item'),
        icon: 'format-gallery',
        category: 'design',
        parent: ['natural/bootstrap5-carousel'],
        example: {},
        edit: function () {
            return el(
                'div',
                useBlockProps({
                    style: {
                        padding: '20px',
                        border: '2px solid #000'
                    }
                }),
                el( InnerBlocks )
            )
        },
        save: function (props) {
            const parentBlocks = select.getBlockParents(props.clientId); // empty in save method, works in console
            const directParent = select.getBlocksByClientId(parentBlocks[parentBlocks.length - 1])[0];
            const siblings = directParent.innerBlocks;

            let classNameSuffix = '';
            if (siblings[0].attributes.clientId === props.clientId) {
                classNameSuffix = ' active';
            }

            return el(
                'div',
                useBlockProps.save({
                    className: 'carousel-item' + classNameSuffix
                }),
                el( InnerBlocks.Content )
            )
        },
    });

Unfortunately, the method I tried returns an error because parentBlocks is empty. Any idea why? The code works in the web console, but appears to be breaking in the save method.