The M2 MacBook Air supports one external display. It can be a very high resolution 5K or 6K display, but there can be only one. There are Mac notebooks that support more external displays, but the M2 MacBook Air uses an entry-level processor chip, and this specification is one thing that goes along with that.
Another issue is that the Targus DSU200TT docking station is a plain USB-C dock – not a Thunderbolt one. Macs do not support DisplayPort MST to the same extent that Windows PCs do. A Mac that supports connecting two or more USB-C or Thunderbolt displays will only support connecting two to the same host port if the device which is attached to that port is a Thunderbolt device (like a Thunderbolt dock). The Mac wants to see a wide Thunderbolt "highway" over which to send the video signals for the two monitors. It's fine if a Thunderbolt dock then splits that "highway" into two smaller "roads".
On the Targus site, there is the footnote
"*HDMI ports support USB-C DP Alt Mode and requires compatible USB-C DisplayPort Alternate Mode host. Supports (2) independent screens in Windows or Chromebook, (1) in iPadOS and (1) in macOS (or dual mirror)"
That "(1) in macOS (or dual mirror)" is what they would expect even if you had a M2 Max MacBook Pro.
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There are workarounds (using DisplayLink and the like) that can let you attach extra displays to a M2 MacBook Air. These work by having you run special software on your Mac to create virtual screens, and send updates to them to a matching "magic decoder ring" chip set in a specially-equipped hub or adapter. None of these workarounds can add more first-class, hardware-supported display outputs, and all may involve compromises.