As per your requirements mentioned in the question, I recommend to use App Service in Microsoft Azure to host your gRPC application. I recommend you to read the following article to understand how can you consider various appservice plan and cost optimizations.
Now the support to host gRPC in Azure App Service, the gRPC support is announced September 2022.
and refer the following link to learn how to publish .Net 6 gRPC application to Azure App Service.
Hope this helps