What's the default color function for BarChart, PieChart?

You can use TracePrint and guess that Blend is being used:

TracePrint[charts[2], _Blend, TraceAction->(Print[InputForm[#]]&)]

HoldForm[Blend[Lighter[System`PlotThemeDump`$ThemeDefaultGradient, 0.2], 0.]]

HoldForm[Blend[{RGBColor[0.982864, 0.7431472, 0.3262672], RGBColor[1., 0.544, 0.2], RGBColor[0.784, 0.47519999999999996, 0.2], RGBColor[0.6754608, 0.4848, 0.7224792], RGBColor[0.4992, 0.5552, 0.8309304]}, 0.]]

...

Confirming @Carl's finding without Trace:

Blend[Lighter[System`PlotThemeDump`$ThemeDefaultGradient, 0.2], #1] &

This is obtained as the setting of the suboption "ChartDefaultStyle" for the default PlotTheme for PieChart:

Charting`ResolvePlotTheme[Automatic, PieChart]

{GridLinesStyle -> Directive[GrayLevel[0.5, 0.4]],   
 LabelStyle -> {GrayLevel[0], FontFamily -> "Arial"},   
 Method -> {"ChartDefaultStyle" ->   
   (Blend[Lighter[System`PlotThemeDump`$ThemeDefaultGradient, 
    0.2], #1] &), "DefaultBoundaryStyle" -> Automatic, 
 "DefaultChartBaseStyle" -> EdgeForm[GrayLevel[0, 0.5]],
"DefaultPlotStyle" -> Automatic}}

System`PlotThemeDump`$ThemeDefaultGradient

% // InputForm

{RGBColor[0.97858, 0.678934, 0.157834], RGBColor[1., 0.43, 0.], 
 RGBColor[0.73, 0.344, 0.], RGBColor[0.594326, 0.356, 0.653099], 
 RGBColor[0.374, 0.444, 0.788663]}

Verifying with a 5-element dataset:

Row[{ PieChart[{1,1,1,1,1}, ImageSize->300], 
   PieChart[{1,1,1,1,1}, ImageSize->300, 
   ChartStyle->Lighter[System`PlotThemeDump`$ThemeDefaultGradient,.2]]}]