Python groupby dataframe and sum datetime[ns] returns NaN

I have a dataframe with different id's and corresponding datetime values. I would like to group by the id and sum all the date time values but I run into several problems. Either the groupby returns NaN or it does not allow me to sum datetime[ns].

This is my dataframe:

data = {'id': [1,2,1,3,4,5,2,6,3], 'date': ['2023-04-13T01:18:11.000000000', '2023-04-10T10:25:03.000000000',
       '2023-03-31T10:30:44.000000000', '2023-04-04T05:51:33.000000000',
       '2023-05-01T23:43:34.000000000', '2023-04-19T09:05:39.000000000',
       '2023-04-12T09:56:50.000000000', '2023-04-28T12:49:23.000000000','2023-04-17T08:10:34.000000000']}
df = pd.DataFrame(data)
df.date = df.date.astype('datetime64[ns]')

I have tried to groupby the id but it sums to NaN:
grouped_df = df.groupby("id", as_index=False)["date"].sum()

If you want to sum the difference between datetimes then you need to calculate the difference between them.

df.date.diff().sum()

In this way, it will calculate the difference between the second and the first, the third and the second... and so on. And then you can sum it.

Pandas diff()

Since you wanted to groupby the whole df by id.

df.groupby('id', as_index=False)['date'].diff().sum()

This will print a single phrase

> Timedelta('2 days 11:03:21')

If you want to use it you need to parse it.