How should I make blur shadows appear with their nodes in a Forest tree in Beamer?

Question

A little while ago, I asked How can I make drop shadows appear with their nodes in a Forest tree in Beamer? At the time, I just eliminated the shadows and went with a shodowless tree. Later, however, I found a very awkward method which worked. A while after that, I received Symbol 1 provided a real answer.

Now I am trying to adapt that solution for my real uses. First, I wanted to make the code conditional on the loading of the appropriate library, so that I can include it in my standard Beamer configuration files.

\makeatletter
\pgfkeysifdefined{/tikz/shadow scale}{%
  % ateb Symbol 1: https://tex.stackexchange.com/a/357412/
  \def\tikzopacityregister{1}%
  \tikzset{
    opacity/.append code={
      \pgfmathsetmacro\tikzopacityregister{#1*\tikzopacityregister}%
    },
    opacity aux/.code={% this is the original definition of opacity
      \tikz@addoption{\pgfsetstrokeopacity{#1}\pgfsetfillopacity{#1}}
    },
    every shadow/.style={opacity aux=\tikzopacityregister}
  }%
}{}
\makeatother

I couldn't find something like \if@tikzlibrary@loaded, so I went with testing for the existence of a PGF key. If there's a way of testing whether a library is loaded, that would obviously be preferable.

Second, I want to make the code work with shadows.blur, so I can use blur shadow as well as drop shadow. The following seems to work, but I'm not sure if it is even vaguely reasonable as a method.

opacity/.append code={
  \pgfmathsetmacro\tikzopacityregister{#1*\tikzopacityregister}%
  \pgfmathsetmacro\pgfbs@opacity{\tikzopacityregister}% cfr: added for blur shadows
},

I tried to append something to, say shadow opacity or to set this when opacity is set. However, I couldn't get this to work and ended up with the above. Again, not great as it relies on an internal implementation detail rather than just the public interface.

I also still get thin outlines of the shadows in this case, but that may be a viewer artefact. (They are still there at 1600% magnification, however, which is the most Okular provides.)

What is the correct way to do this?

\documentclass{beamer}
\usepackage{forest}
\tikzset{% set up for transitions using tikz with beamer overlays - developed by Daniel (https://tex.stackexchange.com/a/55849/) and, in earlier form, by Matthew Leingang (https://tex.stackexchange.com/a/6155/) and modified for this use, I think by Qrrbrbirlbel (https://tex.stackexchange.com/a/112471/)
    invisible/.style={opacity=0,text opacity=0},
    visible on/.style={alt=#1{}{invisible}},
    alt/.code args={<#1>#2#3}{%
      \alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}} % \pgfkeysalso doesn't change the path
    },
}
\forestset{%
  visible with edge from/.style={% based on visible on, developed by Qrrbrbirlbel (https://tex.stackexchange.com/a/112471/)
    /tikz/visible on=<#1->,
    /tikz/every label/.append style={visible on=<#1->},
    edge={/tikz/visible on=<#1->},
  },
}
\usetikzlibrary{shadows.blur}
\makeatletter
\pgfkeysifdefined{/tikz/shadow scale}{%
  % ateb Symbol 1: https://tex.stackexchange.com/a/357412/
  \def\tikzopacityregister{1}%
  \tikzset{
    opacity/.append code={
      \pgfmathsetmacro\tikzopacityregister{#1*\tikzopacityregister}%
      \pgfmathsetmacro\pgfbs@opacity{\tikzopacityregister}% cfr: added for blur shadows
    },
    opacity aux/.code={% this is the original definition of opacity
      \tikz@addoption{\pgfsetstrokeopacity{#1}\pgfsetfillopacity{#1}}
    },
    every shadow/.style={opacity aux=\tikzopacityregister}
  }%
}{}
\makeatother
\begin{document}

\begin{frame}
  \begin{forest}
    for tree={
      draw,
      fill=white,
      blur shadow,
    },
    before typesetting nodes={
      for tree={
        tempcounta/.option=level,
        tempcounta'+=1,
        visible with edge from/.register=tempcounta,
      }
    }
    [first slide
      [second slide[third slide][third slide]]
      [second slide]
    ]
  \end{forest}
\end{frame}
\end{document}