Magento already replied me on the multi-coupon feature.
The product team confirmed that the multicoupon feature is currently available only for use with REST or GraphQL. It is not available for consumption from the storefront with the default Luma theme. The same thing is mentioned in the 2.4.7 release note.
They also requested the doc team to update the configuration document, and also add a note in the backend multicoupon configuration indicating this limitation
Updated: 9May2024
Magento team finally updated the document to explain that it is not available in Storefront.
Official documentation
Determines the maximum number of coupons allowed per order. This feature is available in Admin, GraphQL and REST API only. And it is not available in Storefront.