Here is the feature documentation: https://learn.microsoft.com/en-us/azure/azure-functions/durable/durable-functions-instance-management?tabs=csharp#suspend-and-resume-instances-preview

Here are the equivalent APIs for the .NET in-proc (WebJobs) model:

• https://learn.microsoft.com/en-us/dotnet/api/microsoft.azure.webjobs.extensions.durabletask.idurableorchestrationclient.suspendasync?view=azure-dotnet#microsoft-azure-webjobs-extensions-durabletask-idurableorchestrationclient-suspendasync(system-string-system-string)
• https://learn.microsoft.com/en-us/dotnet/api/microsoft.azure.webjobs.extensions.durabletask.idurableorchestrationclient.resumeasync?view=azure-dotnet#microsoft-azure-webjobs-extensions-durabletask-idurableorchestrationclient-resumeasync(system-string-system-string)