Can you use Thunderbolt for Screen Sharing?

I recently broke the screen on my Early 2020 MacBook Air, however I still can use my 2018 MacBook Air. I still use my broken Mac by screen sharing over VNC, however, since VNC uses Wi-Fi, the picture occasionally lags, and I get no audio. Before I broke my Mac, I was going to buy a thunderbolt cable to connect the two Macs for file transfers. I need to know if I can share my screen via thunderbolt instead of Wi-Fi in any way. Using HDMI is generally annoying since the monitor I own has an extremely low resolution compared to the retina screen, and I only have the Multiport Adapter as a USB dongle for both Macs. I need to know if I can use the thunderbolt dongle to somehow access my other Mac.

I've heard some people used thunderbolt to create a network between the two Macs, but that would still leave network lag. I've also heard people use Target Disk Mode, though I've only seen people do it when both Macs are the same model.

In case this is important, the Mac would try to boot from has a macOS version supported by both devices, Catalina.