Do I get the Elastic Cloud on Azure cheaper with SQL Server Core licenses?

Question

I have seen that companies with SQL server core licenses do get Azure Cloud cheaper (sometimes even for the infrastructure costs), but is that also possible for the Elasticsearch Service on the Elastic Cloud? Or is it also possible to host Elasticsearch on Azure or GCP without the Elastic Cloud? Everytime I search for comparison of the cloud providers, I only find a comparison between Opensearch (AWS Elasticsearch Service) and the Elastic Cloud. I Also find on the Elasticsearch webpage, that AWS, Azure and GCP can be used to provide the ELastic Cloud. But I do not understand if I can only use the a cloud server to run a managed service without the Elastic Cloud (which costs really much).