Touchbar stopped working and a fuse burned?

So. I have never seen this issue on a Touchbar, But this is actually an extremely common issue in various iterations.

To start, that is the connector for the Touchbar's touchscreen. Which is likely why it's not working. For point of reference, the one for the display bit of the Touchbar is the one all the way in the bottom right corner, near the speaker.

The component on the board that is charred, is on an electrical line called PP5V_GS3. This is a 5 volt line, which supplies power to touch components in the touch bar (and others). The component itself is a small inductor that does act much like a fuse in this particular case.

Usually this occurs when a connector is plugged in or unplugged when the battery for the device is still connected. But it could be due to poor seating on the cable, or the connector (on either side) having some damage. But regardless. The PP5V_GS3 line ended up shorting to ground, which means rather than its normal path, it was getting a direct, little or no resistance path to ground. Usually that ends in more current being drawn than some component is rated for and it blows. Like the the little inductor on your board.

If you notice in your picture, aside from the pin to pointed to, there is another both on the board side, and the cable side that have clearly seen some heat. That will be your actual issue. That's the connector correlation to the burned inductor.

Realistically you'll need to replace the burned component at a minimum. But could be more depending on how the short actually occurred. It's hard to tell for sure just from pictures and your description. You may need to enlist someone with some soldering know how to help with this one if that's not in your current skill set.