View Transition currently automatically animates an elements size/transform. backdrop-filter should probably also be in this list. Its a property of how the element renders where its embedded, not the element's content itself. Same discussion as mix-blend-mode: #8962.

With mix-blend-mode we don't set up an animation because it can't be interpolated but backdrop-filter can.

Here's an example: https://codepen.io/LukyVj/pen/MWZovLb. The following bit of CSS fixes the issue, which can be done automagically by the browser.

nav {
  view-transition-name: nav;
}

::view-transition-group(nav) {
  backdrop-filter: blur(3px);
}