Why is my second monitor showing "No Signal" when connected to MacBook Air?

In order to get the external monitor (video output) ~ you will need to use "Thunderbolt 2" --> "whatever interface (VGA, HDMI...etc) adapter"

USB 3 -> HDMI adapter will not work for 2017 MacBook Air.

Best

USB-A was never designed as a video interface, and does not carry video signals.

If you have a USB 3.0 to HDMI adapter, it no doubt drives its output in a second-class way, requires the installation of a special driver on your computer, and may come with significant compromises. If you cannot get, or do not install, a special driver that is compatible with your Mac, there will be no video output.

Best Buy – Insignia USB to HDMI Adapter

If you go to the Best Buy product page, then click Features, some links come up, including a link for "Firmware, Drivers & Software (Mac) (Zip)". I don't know if this stuff works with macOS 12.7 (Monterey) or Apple Silicon Macs, as the top of the feature panel mentions macOS 10.12 (Sierra), a much older version of macOS.

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A better way to connect a monitor would be using hardware video output. Your computer supports attaching a single external monitor with a resolution of up to 3840 x 2160 @ 60 Hz.

MacBook Air (13-inch, 2017) - Technical Specifications - Apple Support

It has an old-style Thunderbolt 2 port, with a Mini DisplayPort connector, that can double as a Mini DisplayPort. If your monitor has a DisplayPort input, you could hook your Mac directly to it with a Mini DisplayPort to DisplayPort cable. If the monitor only has a HDMI input, you could get a Mini DisplayPort to HDMI adapter.