HowTo vertically center node labels in Graph output

Version: "14.3.0 for Linux x86 (64-bit) (July 8, 2025)"

The code listed below using the data following it produces the result shown in the image. I want the node labels positioned directly to the right of the labeled nodes. I really only want that for the leaf nodes. But I need to start somewhere. How can this be accomplished.

In a sandbox directory create and save a Mathematica notebook with the following content.

Module[{g, emb, scaledEmb, embF}
 , SetDirectory[NotebookDirectory[]];
 g = Import["ss01-05-sentence-leafnodes.gv", "Graph"];
 embF[g_] := GraphEmbedding[g
   , {"LayeredDigraphEmbedding", "Orientation" -> Left, 
    "RootVertex" -> "CH"}];
 emb = Map[{#[[1]]/2, -#[[2]]} &, embF[g]];
 scaledEmb = Map[{#[[1]]/2, #[[2]]} &, emb];
 Graph[g
  , VertexCoordinates -> scaledEmb
  , VertexLabels -> 
   Placed["Name", {Right, Center}, Offset[{5, 0}, #] &]
  , VertexSize -> 0.1
  , EdgeStyle -> Directive[Arrowheads[0.025]]
  , VertexLabelStyle -> Directive[FontSize -> 8, Background -> White]
  , ImageSize -> Large
  , ImagePadding -> {{50, 200}, {50, 50}} ]]

In the same directory as the Mathematica notebook create a file named ss01-05-sentence-leafnodes.gv with the following content:

digraph DocumentStructure {
  rankdir=TB;
  node [shape=record];
  CH [label="CH"];
  S01 [label="S01"];
  S01P01 [label="S01P01"];
  S01P01T01 [label="S01P01T01"];
  S01P01T02 [label="S01P01T02"];
  S01P01T03 [label="S01P01T03"];
  S01P01T04 [label="S01P01T04"];
  S01P01T05 [label="S01P01T05"];
  S01P01T06 [label="S01P01T06 | LN01"];
  S01P01T07 [label="S01P01T07"];
  S01P01T08 [label="S01P01T08"];
  S01P01T09 [label="S01P01T09"];
  S01P01T10 [label="S01P01T10"];
  S01P01T11 [label="S01P01T11"];
  S01P01T12 [label="S01P01T12 | LN02"];
  S01P02 [label="S01P02"];
  S01P02T01 [label="S01P02T01"];
  S01P02T02 [label="S01P02T02"];
  S01P03 [label="S01P03"];
  S01P03T01 [label="S01P03T01"];
  S02 [label="S02"];
  S02P01 [label="S02P01"];
  S02P01T01 [label="S02P01T01"];
  S02P01T02 [label="S02P01T02"];
  S02P01T03 [label="S02P01T03"];
  S02P01T04 [label="S02P01T04"];
  S02P01T05 [label="S02P01T05 | LN03"];
  S02P02 [label="S02P02"];
  S02P02T01 [label="S02P02T01"];
  S02P03 [label="S02P03"];
  S02P03T01 [label="S02P03T01"];
  S02P03T02 [label="S02P03T02"];
  S02P03T03 [label="S02P03T03"];
  S02P04 [label="S02P04"];
  S02P04T01 [label="S02P04T01"];
  S02P05 [label="S02P05"];
  S02P05T01 [label="S02P05T01"];
  S02P05T02 [label="S02P05T02"];
  S02P06 [label="S02P06"];
  S02P06T01 [label="S02P06T01"];
  S02P07 [label="S02P07"];
  S02P07T01 [label="S02P07T01"];
  S02P08 [label="S02P08"];
  S02P08T01 [label="S02P08T01"];
  S02P08T02 [label="S02P08T02"];
  S02P08T03 [label="S02P08T03 | LN04"];
  S03 [label="S03"];
  S03P01 [label="S03P01"];
  S03P01T01 [label="S03P01T01"];
  S03P01T02 [label="S03P01T02"];
  S03P01T03 [label="S03P01T03"];
  S03P01T04 [label="S03P01T04 | LN05"];
  CH -> S01;
  S01 -> S01P01;
  S01P01 -> S01P01T01;
  S01P01 -> S01P01T02;
  S01P01 -> S01P01T03;
  S01P01 -> S01P01T04;
  S01P01 -> S01P01T05;
  S01P01 -> S01P01T06;
  S01P01 -> S01P01T07;
  S01P01 -> S01P01T08;
  S01P01 -> S01P01T09;
  S01P01 -> S01P01T10;
  S01P01 -> S01P01T11;
  S01P01 -> S01P01T12;
  S01 -> S01P02;
  S01P02 -> S01P02T01;
  S01P02 -> S01P02T02;
  S01 -> S01P03;
  S01P03 -> S01P03T01;
  CH -> S02;
  S02 -> S02P01;
  S02P01 -> S02P01T01;
  S02P01 -> S02P01T02;
  S02P01 -> S02P01T03;
  S02P01 -> S02P01T04;
  S02P01 -> S02P01T05;
  S02 -> S02P02;
  S02P02 -> S02P02T01;
  S02 -> S02P03;
  S02P03 -> S02P03T01;
  S02P03 -> S02P03T02;
  S02P03 -> S02P03T03;
  S02 -> S02P04;
  S02P04 -> S02P04T01;
  S02 -> S02P05;
  S02P05 -> S02P05T01;
  S02P05 -> S02P05T02;
  S02 -> S02P06;
  S02P06 -> S02P06T01;
  S02 -> S02P07;
  S02P07 -> S02P07T01;
  S02 -> S02P08;
  S02P08 -> S02P08T01;
  S02P08 -> S02P08T02;
  S02P08 -> S02P08T03;
  CH -> S03;
  S03 -> S03P01;
  S03P01 -> S03P01T01;
  S03P01 -> S03P01T02;
  S03P01 -> S03P01T03;
  S03P01 -> S03P01T04;
}