In safari extension, fail to register serviceWorker

I'm developing an extension for manifest v3 on iOS 15.5 and 15.6 simulator. manifest.json is as follows

 "background": {
    "service_worker": "background.js",
 },

In the background page developer tool

navigator.serviceWorker.register('safari-web-extension://xxx/background.js');

but It looks like the serviceWorker register is not working properly.

This works on IOS 16 and above, by the way.