changepoint-detector already used the Nile series as its example. A new test now pins what happens on it under four settings: level change, level change allowing for autocorrelation (--ar1), level-and-volatility, and the robust version of that. All four return a single change at 1899, the first full year after the 1898 dam works (Cobb 1978), and every 95% range holds 1899.
The settings differ in how sure they are. Plain mean gives a range of 1897 to 1899 and 79% Bayesian probability. --ar1 gives 1897 to 1901 and 50%, because flow in one year predicts the next, so fewer years are independent evidence. The date doesn't move; the confidence does. That is the behaviour you want from an autocorrelation allowance.
One series, one documented break: it shows the settings agree here, not that they agree everywhere. Statistical analysis of supplied data, not advice.