Annotations in groupedbar are broken?

Specific Domains Visualization
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2

You should open an issue in StatsPlots.jl.

Meanwhile, you may check this wrapping function (not fully tested):

Code 
function annotated_groupedbar(xx, yy, group; series_annotations="", legend=:top_right, bar_width=0.8, color=:blue, font_size=10)
    gp = groupedbar(xx, yy, group=group, series_annotations="", legend=legend, bar_width=bar_width)
    m = length(unique(group))       # number of items per group            
    n = length(unique(xx))          # number of groups
    xt = (1:n) .- 0.5               # plot x-coordinate of groups' centers
    dx = bar_width/m                # each group occupies bar_width units along x
    dy = diff([extrema(yy)...])[1]
    x2 = [xt[i] + (j - m/2 - 0.5)*dx for j in 1:m, i in 1:n][:]
    k = 1
    for i in 1:n, j in 1:m
        y0 = gp[1][2j][:y][i] + 0.04*dy
        if isfinite(y0)
            annotate!(x2[(i-1)*m + j], y0, text(series_annotations[k], :center, color, font_size))
            k += 1
        end
    end
    gp
end

For your example it produces:

using StatsPlots
x, y = ["A","A","B","B"], [1,2,3,4]
year = ["2020","2021","2020","2021"]
annotated_groupedbar(x, y, year; series_annotations=y, legend=:topleft, bar_width=0.7, color=:blue, font_size=10)

StatsPlot_groupedbar_custom_annotation_OP_ex

And for other more interesting groupings with gaps:

using StatsPlots
x, y = ["D","A","A","B","B","C","C","C","D"],  collect(1:9)
year = ["2020","2021","2022","2020","2022","2020","2021","2022","2021"]

annotated_groupedbar(x, y, year; series_annotations=y, legend=:topleft, bar_width=0.7, color=:blue, font_size=10)

annotated_groupedbar(year, y, x; series_annotations=y, legend=:topleft, bar_width=0.7, color=:blue, font_size=10)

StatsPlot_groupedbar_custom_annotation

StatsPlot_groupedbar_custom_annotation2

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