I am summarizing the details discussed in the comments and providing an answer.
The warning message can be ignored as the function host is starting and the http triggered function is running successfully. We see this message as the core tools might be checking for updates and failing due to lack of network connectivity.
Please note that function core tools would work on local environment even when there is no internet connection. Please make sure to use latest version of function core tools
https://learn.microsoft.com/en-us/azure/azure-functions/functions-run-local?tabs=v4%2Cwindows%2Ccsharp%2Cportal%2Cbash#install-the-azure-functions-core-tools