I did a CSS experiment back in 2008 (before CSS allowed for backdrop-blur) that did the same'ish effect: https://webdev.andersriggelsen.dk/aero/
It works by using a fixed-position pre-blurred (with glass effects) background image: https://webdev.andersriggelsen.dk/aero/bgl.jpg
This is a lot more performant than a live gaussian blur but it of course has all the drawbacks of not allowing for a dynamic background image.
I took it one step further even earlier using a Flash file as a backdrop which was able to achieve the glass effect while still being in a dynamic moveable frame. Can't recall if it used iframes, would need to dig up the code but considering the era it probably did.
The floating window doesn't update for me past the initial position. Windows 10 19045.5131. Chrome is up to date Version 131.0.6778.86 (Official Build) (64-bit)
That is quite strange Chrome behavior. Seems to only update it's background position when the window size changes. Looks like a Chrome bug to me! Probably some optimization effort that went wrong. I'm quite sure that it worked back in the days in Chrome.
This works as expected in Firefox.