I believe you'll find forecastHybrid package very useful for this purpose. See below:
library(forecast)
#Data
gini <- c(21.8, 23.3, 23.4, 25.5, 27.1, 31.2, 34.9, 35.2, 39.7, 28.4, 32.2, 42.1, 46.2)
#As TS
Xt <- ts(data = gini,
start = 2003,
end = 2015,
frequency = 1)
#ETS
ets.gini <- ets(y = Xt)
forecast.ets.gini <- forecast.ets(object = ets.gini,
h = 6,
level = 95,
PI = TRUE)
plot(x = forecast.ets.gini,
lwd = 3,
main = "",
col = "black",
xlab = "Year",
ylab = "Gini",
xlim = c(2000,2025),
ylim = c(0, 100),
panel.first = grid(),
showgap = FALSE,
shaded = TRUE,
shadebars = FALSE,
shadecols = "grey75",
fcol = "grey50",
flwd = 3)

#ARIMA
arima.gini <- auto.arima(Xt)
forecast.arima.gini <- forecast(object = arima.gini,
h = 6,
level = 95)
plot(x = forecast.arima.gini,
lwd = 3,
main = "",
col = "black",
xlab = "Year",
ylab = "Gini",
xlim = c(2000, 2025),
ylim = c(0, 100),
panel.first = grid(),
showgap = FALSE,
shaded = TRUE,
shadebars = FALSE,
shadecols = "grey75",
fcol = "grey50",
flwd = 3)

#Combination
library(forecastHybrid)
#> Loading required package: thief
hybrid_model <- hybridModel(y = Xt,
models = c("ae"),
weights = "equal")
#> Fitting the auto.arima model
#> Fitting the ets model
hybrid_model_forecast <- forecast(object = hybrid_model,
h = 6,
level = 95,
PI.combination = "mean")
plot(x = hybrid_model_forecast,
lwd = 3,
main = "",
col = "black",
xlab = "Year",
ylab = "Gini",
xlim = c(2000, 2025),
ylim = c(0, 100),
panel.first = grid(),
showgap = FALSE,
shaded = TRUE,
shadebars = FALSE,
shadecols = "grey75",
fcol = "grey50",
flwd = 3)

Created on 2019-04-09 by the reprex package (v0.2.1)
Note that these forecasts indeed match what you've calculated manually:
> mean.gini <- (forecast.ets.gini$mean + forecast.arima.gini$mean) / 2
> lower.gini <- (forecast.ets.gini$lower + forecast.arima.gini$lower) / 2
> upper.gini <- (forecast.ets.gini$upper + forecast.arima.gini$upper) / 2
>
> cbind(mean.gini,
+ lower.gini,
+ upper.gini)
Time Series:
Start = 2016
End = 2021
Frequency = 1
mean.gini lower.gini upper.gini
2016 46.19979 34.02411 58.37547
2017 46.19979 28.91875 63.48084
2018 46.19979 24.95775 67.44184
2019 46.19979 21.58144 70.81814
2020 46.19979 18.57375 73.82583
2021 46.19979 15.82419 76.57540
>
> hybrid_model_forecast
Point Forecast Lo 95 Hi 95
2016 46.19979 34.02411 58.37547
2017 46.19979 28.91875 63.48084
2018 46.19979 24.95775 67.44184
2019 46.19979 21.58144 70.81814
2020 46.19979 18.57375 73.82583
2021 46.19979 15.82419 76.57540
Hope this helps.
Note: I see you're using ; at the end of the lines. These are not necessary in R.