The rendering of elements with filters is currently done before the rendering of the cameras, which means that the render pass result won't be yet available for the filtered elements.
We have a future feature which involves integrating the rendering of filters with render graph. Once done, the result of a custom pass could be integrated with the filtered elements.
Short-term, a workaround for you would be to use the previous frame blurred scene instead of the current frame. This has the downside of being one-frame-late, of course. But this may be acceptable for a background blur effect.