Here is what my webview scrollbars look like in 1.89.1:

Here is what they look like in 1.90-insiders:

Looks styled still based on the colors, just different rendering

They really don't look that similar (other than the colors are close) -- in the first the scrollbar has no corners (arrows) is much thinner, and what you can't tell in the screenshot is that it behaves just like other VS Code scrollbars in that it hides and fades based on hover/focus.

While in Insiders none of those style are taking affect -- it seems ::-webkit-scrollbar* properties don't seem to apply anymore.
So we seem to be stuck with almost standard platform scrollbars.

Version: 1.90.0-insider (Universal)
Commit: 81c89c4
Date: 2024-05-22T09:32:21.946Z
Electron: 29.3.1
ElectronBuildId: 9464424
Chromium: 122.0.6261.156
Node.js: 20.9.0
V8: 12.2.281.27-electron.0
OS: Darwin arm64 22.6.0

I see a similar issue.

1. Executing Webview View API Sample: https://github.com/microsoft/vscode-extension-samples/tree/main/webview-view-sample
2. The background color of the scrollbar is white.

A workaround is adding the following to main.css:

html {
	scrollbar-color: var(--vscode-scrollbarSlider-background) var(--vscode-sideBar-background);
}

Adding ::-webkit-scrollbar* doesn't work.