I faced this issue with Node V16.17.0 and azure function core tools V4*
I used command to trace logs
func host start --verbose
Then I saw in logs that it's trying to download Microsoft.Azure.Functions.ExtensionBundle.zip
(with some version) to specific folder. In my case it was Microsoft.Azure.Functions.ExtensionBundle.2.13.0.zip
I manually downloaded that file and extracted zip to downloads folder.
Then I sas in logs that before downloading this zip file, It is checking if this file already exists in temp folder and in users folder as well. In my case it was
C:\Users\<UserID>\.azure-functions-core-tools\Functions\ExtensionBundles\Microsoft.Azure.Functions.ExtensionBundle
and
C:\Users\UserID>\AppData\Local\Temp\Functions\ExtensionBundles\Microsoft.Azure.Functions.ExtensionBundle\2.18.0
Make sure to create folder structure as well if not present.
I just copied contents from extracted folder to this mentioned location.
It worked.