Make a customized filter on a grouped dataframe with multiple conditions

Please find below my input/desired output :

INPUT

      Id   Status        Date
0  Id001      off  01/01/2022
1  Id001   online  01/06/2022
2  Id002      off  05/12/2021
3  Id002      off  30/08/2021
4  Id003  running  02/03/2021
5  Id004   online  21/10/2021
6  Id004  running  01/04/2022
7  Id005   online  01/02/2022
8  Id005   online  02/07/2022

OUTPUT (desired)

      Id   Status        Date
0  Id001   online  01/06/2022
1  Id002      off  05/12/2021
2  Id003  running  02/03/2021
3  Id004   online  21/10/2021
4  Id005   online  01/02/2022

The goal is firstly to have one line per Id in the output.
The output will be made based on a this simple statement :

if a group of Id has «online» as a Status then:  
    if «online» occurences > 1 then: 
        Choose the oldest Id that has «online»
    else:  
        choose the Id that has «online»
else:
    Choose the most recent Id

This is what I’ve tried so far :

import pandas as pd
import numpy as np

df = pd.DataFrame({'Id': ['Id001','Id001','Id002','Id002','Id003','Id004','Id004','Id005','Id005'],
                    'Status': ['off','online','off','off','running','online','running','online','online'],
                    'Date': ['01/01/2022','01/06/2022','05/12/2021','30/08/2021','02/03/2021','21/10/2021','01/04/2022','01/02/2022','02/07/2022']})

df.groupby(['Id', 'Status'], as_index=False).agg({'Date' : [np.min, np.max]}).reset_index()

Do you have any suggestion/propositions, please ?
Any help we be so much appreciated !

Answer

Answer is completely edited – first filter only online rows, sorting by Date and remove duplicates by first Id:

df1 = df[df['Status'].eq('online')].sort_values('Date').drop_duplicates('Id')
print (df1)
      Id  Status       Date
5  Id004  online 2021-10-21
7  Id005  online 2022-02-01
1  Id001  online 2022-06-01

Then filter not matched Id and sorting descending:

df2 =df[~df['Id'].isin(df1['Id'])].sort_values('Date',ascending=False).drop_duplicates('Id')
print (df2)
      Id   Status       Date
2  Id002      off 2021-12-05
4  Id003  running 2021-03-02

Last join both Dataframes:

df = pd.concat([df1, df2]).sort_values('Id', ignore_index=True)
print (df)
      Id   Status       Date
0  Id001   online 2022-06-01
1  Id002      off 2021-12-05
2  Id003  running 2021-03-02
3  Id004   online 2021-10-21
4  Id005   online 2022-02-01

Original solution should be changed:

df['Date'] = pd.to_datetime(df['Date'], dayfirst=True)

df1 = (df.assign(s = df['Status'].eq('online')).groupby(['Id','s'])
         .agg(Date_min=('Date','idxmin'), Date_max=('Date','idxmax')))

df1 = df1[~df1.index.get_level_values(0).duplicated(keep='last')].reset_index()
print (df1)
      Id      s  Date_min  Date_max
0  Id001   True         1         1
1  Id002  False         3         2
2  Id003  False         4         4
3  Id004   True         5         5
4  Id005   True         7         8

df = df.loc[np.where(df1['s'], df1['Date_min'], df1['Date_max'])]
print (df)
      Id   Status       Date
1  Id001   online 2022-06-01
2  Id002      off 2021-12-05
4  Id003  running 2021-03-02
5  Id004   online 2021-10-21
7  Id005   online 2022-02-01