Jeremy's option to query App Insights logs will work, but there is a delay- this might be fine for your purposes.
There are a couple endpoints in the Azure REST API that can give you useful info:
If you are using a plan that scales at the App Service level the it's GET method will return info on the number of instances:
GET https://management.azure.com/subscriptions/{subscriptionId}/resourceGroups/{resourceGroupName}/providers/Microsoft.Web/serverfarms/{name}?api-version=2021-02-01
Under the Web Apps API, you can get instance info for your function app currently even on consumption plan:
GET https://management.azure.com/subscriptions/{subscriptionId}/resourceGroups/{resourceGroupName}/providers/Microsoft.Web/sites/{name}/instances?api-version=2021-02-01
If you are looking for the current number of processes (since there can be more than one per instance), you can take the IDs from the previous query to get the processes.
GET https://management.azure.com/subscriptions/{subscriptionId}/resourceGroups/{resourceGroupName}/providers/Microsoft.Web/sites/{name}/instances/{instanceId}/processes?api-version=2021-02-01