What do you mean by "dual-screen" extender?
If you mean one that adds two screens, one on either side of the laptop display, a M3 MacBook Air cannot drive both screens of such an extender in a hardware-supported way.
The M3 MacBook Airs support one external display with the lid open, two with the lid closed. That is based on the hardware built into the plain M3 chip itself. No external device can increase the limit. Even if it's not quite what you want, this limit is an improvement over the one external display limit of the M1 and M2 MacBook Airs.
To drive two external displays, you will need to use a second-class workaround – such as DisplayLink – to drive one or both of them. Note that such workarounds require both a special chip set in the hub, adapter, or display – and a matching driver on the Mac. Neither the special chip set alone, nor the driver alone, will get you any extra displays. Workarounds may have drawbacks that you would not encounter with hardware-supported video output.