How can I extend across two monitors or have separate dual monitors for my MacBook?

There are no hubs or adapters that you can attach to your M2 MacBook Air to add first class, hardware-accelerated display outputs. That machine will always have just two such outputs – one dedicated to the built-in display, leaving one free for an external display.

There are workaround technologies – like DisplayLink – that can let you attach more displays in a second-class way. These create virtual displays in software and send updates to "magic decoder ring" chips in suitably-equipped hubs or adapters. There may be drawbacks like artifacts, lags, unsuitability for fast-changing content, and blank screens when trying to view DRM-infested streaming video (e.g., from a commercial movie site). But some people find this type of workaround useful for attaching displays that will be used for relatively static content.

Three examples of such adapters are:

Other World Computing – OWC USB-C Dual HDMI 4K Display Adapter with DisplayLink

SonnetTech – DisplayLink Dual HDMI Adapter for M Series Macs

SonnetTech – DisplayLink Dual DisplayPort Adapter for M Series Macs

Synaptics is the company that supplies the DisplayLink decoder chip sets in the adapters, and the software that you must run on your Mac in order to make the adapters work.

Synaptics – DisplayLink Graphics

Issue #1

The 13" and 15" M2 MacBook Airs only support one external display.

MacBook Air (M2, 2022) - Technical Specifications - Apple Support

MacBook Air (15-inch, M2, 2023) - Technical Specifications - Apple Support

Issue #2

Macs do not support DisplayPort MST daisy-chaining. To connect two displays to a single Mac host port, on a Mac that supports multiple external displays, that port has to be a Thunderbolt port, and the device attached to it has to be a Thunderbolt device, such as a Thunderbolt dock. (There are Thunderbolt docks that permit you to attach two non-Thunderbolt displays or adapters with resolutions and refresh rates of up to 4K @ 60 Hz each.)