I don't think I've ever seen this feature ever before (keeping in mind that the purpose of the tool is to draw smooth lines, and there would probably be another tool for drawing signatures). It's quite brilliant!

Photoshop has had it for quite a while now. It's titled brush smoothing

Does it have the leading drag handle? That's the brilliant part. My ancient copy of Photoshop has a smoothed brush; but it doesn't have the leading drag handle.

Kind of. You can click a gear and set various options on it, including a "pulled string mode", which works similarly to this, where it has a "smoothing radius" that movement within will not change cursor direction, and then a "stroke catch up" mode where the stroke is at a somewhat constant speed, regardless of how you move your mouse.

The former looks like this https://i.imgur.com/TGE7N1z.png

Lazy Nezumi has been around since 2009. Stabilisers,etc. are a lot more prominent in the digital art community.

Yes! That's it! :-)