I want to get the content-transfer size like in chrome devtool network tab through chrome extension API but it doesn't have events for this.

Also checked webRequest API.
I want to get the content-transfer size like in chrome devtool network tab through chrome extension API but it doesn't have events for this.

Also checked webRequest API.
DevTools itself uses CDP (Chrome DevTools Protocol) events like Network.responseReceived and its encodedDataLength field (source).
It can be used in an extension via chrome.debugger API:
Network.enableNetwork.responseReceivedAn annoying side-effect is that Chrome shows a warning in all tabs when the debugger is used by an extension. If you need more info, search for chrome.debugger examples yourself (here's a few official ones) and inspect the source code of devtools.
Another approach is to use Content-Length HTTP header but it's not guaranteed to be present on all responses: here's an example that you can further enhance with a check for fromCache field that's provided in a separate onCompleted event.