Is autocorrelation an indication of Non Stationary Series

[Khurram]

I have time series data and it has following Autocorrelation plot for each lag , x is lag number and y is correlation

I read https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/time-series/how-to/... 

at bottom of this link

"A stationary time series has a mean, variance, and autocorrelation function that are essentially constant through time. The data is non-stationary when there is a large spike at lag 1 that slowly decreases over several lags. If you see this pattern, you should difference the data before you attempt to identify a model. To difference the data, use differences. Once you difference the data, obtain another autocorrelation plot."

I have two confusion please clear my confusion

1) Do we really need to have constant autocorrelation for each lag for data to be stationary?

2) Is my above data series does not have constant autocorrelation?

Thanks

[Khurram]

one document here which says the same https://online.stat.psu.edu/stat510/lesson/1/1.2