Thanks for asking question! Yes, the data source can be created out of a storage account on any subscription (even in a subscription in a different tenant).
We recommend to check for firewall configurations on both the search service and storage account.
Check: https://video2.skills-academy.com/en-us/azure/hpc-cache/hpc-cache-blob-firewall-fix
https://video2.skills-academy.com/en-us/azure/search/service-configure-firewall
Also, Check the SKU limits: https://video2.skills-academy.com/en-us/azure/search/search-limits-quotas-capacity#indexer-limits
Depending on the SKU, there are limits for the amount of data sources that can be created.
Let us know incase further query or issue remains.