Unable to connect MacBook Air M3 to a Dell 3100 USB 3.0

Your docking station connects to a computer via a USB 3.0 B port. USB-A and USB-B were never meant to carry video signals. So even though your computer is capable of driving external monitor(s) (one with the lid open, two with the lid closed) via USB-C (DisplayPort) or Thunderbolt, you're using a dock that doesn't have what it takes to work with standard USB-C (DisplayPort) or Thunderbolt output from any computer (Mac or PC).

Presumably the way you get this thing to work is to install special software on your computer, software that creates virtual displays, and pushes updates out over a narrow USB 3.0 pipe.

Dell – Dell Docking Station USB 3.0 D3100 User's Guide

Sure enough, the manual refers to installing DisplayLink drivers for Windows 7, 8, 8.1, and 10. The manual makes no promises of Mac support. You probably could get the dock to work by installing Mac DisplayLink software, from the Synaptics site. (Synaptics supplied the DisplayLink chip set that Dell used in that dock.)

Synaptics – DisplayLink Downloads

DisplayLink – Troubleshooting: macOS

My recommendation would be to forget it, and get a proper USB-C or Thunderbolt dock. One that doesn't require you to install special software, and that doesn't try to shoehorn video over a small USB 3.0 pipe.

Your MacBook Air supports one external monitor with the lid open, to two with the lid closed. Apple's Technical Specifications spell that out very clearly.

There is no adapter, dock, or software that can add more first-class, hardware-supported video outputs. If you needed to drive the built-in display, and two external displays, simultaneously, in a proper way, you should have purchased a MacBook Pro that had a M3 Pro or M3 Max chip.

As far as workarounds go, DisplayLInk-based workarounds are common, but your D3100 starts out with a couple of strikes against it. It connects via USB 3.0 (not USB 3.1 Gen 2), so you are throwing away half of the bandwidth that your Mac could have easily provided. It's an old dock – the copyright date in the manual is 2014. Also, Dell does not seem to be particularly interested in providing support for Mac users.

Dell KnowledgeBase – Dell DisplayLink Docking Stations and macOS Support

"Dell is providing this information but does not provide software support for Apple products."