Sort of a workaround:
data = {{{2020, 7, 29, 22, 30}, 0}, {{2020, 7, 29, 22, 45}, 
    2}, {{2020, 7, 29, 22, 58}, 3}, {{2020, 7, 29, 23, 0}, 
    2}, {{2020, 7, 29, 23, 8}, 2}, {{2020, 7, 29, 23, 39}, 
    3}, {{2020, 7, 29, 23, 40}, 3}, {{2020, 7, 30, 2, 38}, 
    2}, {{2020, 7, 30, 2, 42}, 2}, {{2020, 7, 30, 2, 47}, 
    2}, {{2020, 7, 30, 2, 48}, 2}, {{2020, 7, 30, 2, 49}, 
    2}, {{2020, 7, 30, 5, 5}, 4}, {{2020, 7, 30, 5, 6}, 
    4}, {{2020, 7, 30, 5, 7}, 3}, {{2020, 7, 30, 5, 51}, 
    2}, {{2020, 7, 30, 5, 52}, 3}, {{2020, 7, 30, 5, 53}, 
    2}, {{2020, 7, 30, 5, 54}, 3}, {{2020, 7, 30, 5, 55}, 
    3}, {{2020, 7, 30, 6, 32}, 2}, {{2020, 7, 30, 6, 33}, 
    3}, {{2020, 7, 30, 6, 34}, 3}, {{2020, 7, 30, 6, 35}, 0}};
colorRange = {Green, Blue, Red, Blue, Blue, Blue, Blue, Red, Red, Red,
    Red, Red, Red, Red, Red, Red, Red, Red, Red, Red, Red, Red, Red, 
   Green};
pos = Map[Flatten, 
   Position[colorRange, #] & /@ {Green, Blue, Red}, {1}];
ptgrn = data[[#]] & /@ pos[[1]];
ptblu = data[[#]] & /@ pos[[2]];
ptred = data[[#]] & /@ pos[[3]];
DateListPlot[{ptgrn, ptblu, ptred}, AspectRatio -> 0.8/3, 
 Filling -> Axis, 
 FrameTicks -> {Automatic, {{{{2020, 7, 29, 22, 30}, "\!\(\*
      StyleBox[\"22\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
      StyleBox[\":\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
      StyleBox[\"30\",\nFontColor->RGBColor[1, 0, 0]]\)"}, {{2020, 7, 
       29, 23, 00}, "23:00"}, {{2020, 7, 29, 24, 00}, 
      "24:00"}, {{2020, 7, 30, 01, 00}, 
      "01:00"}, {{2020, 7, 30, 02, 00}, 
      "02:00"}, {{2020, 7, 30, 03, 00}, 
      "03:00"}, {{2020, 7, 30, 04, 00}, 
      "04:00"}, {{2020, 7, 30, 05, 00}, 
      "05:00"}, {{2020, 7, 30, 06, 00}, 
      "06:00"}, {{2020, 7, 30, 06, 35}, "\!\(\*
      StyleBox[\"06\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
      StyleBox[\":\",\nFontColor->RGBColor[1, 0, 0]]\)\!\(\*
      StyleBox[\"35\",\nFontColor->RGBColor[1, 0, 0]]\)"}}, None}}, 
 ImageSize -> 600, Joined -> False, 
 LabelStyle -> Directive[Black, Bold, 10], 
 PlotStyle -> {{PointSize[.02], Green}, {PointSize[.015], 
    Blue}, {PointSize[.0095], Red}}]