Hi Ramrez,
I believe that this is what you are looking for:
"Azure Functions offers an integration with Azure Monitor Logs to monitor functions. This article shows you how to configure Azure Functions to send system-generated and user-generated logs to Azure Monitor Logs."
Source : https://learn.microsoft.com/en-us/azure/azure-functions/functions-monitor-log-analytics?tabs=csharp
Instead of sending it to "log analytics" you can archive it to a "storage account".
You then need a client tool that works with Azure Storage.
https://learn.microsoft.com/en-us/azure/storage/common/storage-explorers
Let me know if that helps.