read edit on bottom and other answers/comments!
I've found few different implementations of NestedWebView and noticed that all of them are old and implements NestedScrollingChild when currently we have 3rd version of this interface: NestedScrollingChild3 (androidx). So I've penetrated current version of NestedSrcollView and I've added some new methods handling, and now it works :). To be exact - I was trying to achieve smooth scroll through whole screen just like when WebView would fill whole screen and Toolbar was part of web content (always on top). Also snap is working :). use wisely