SQL Server 2016

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Set DateFormat DMY
Declare @YourTable Table ([USER_ID] int,[CONTRACT_ID] int,[START_DATE] date,[END_DATE] date)
Insert Into @YourTable Values 
 (1,14,'18.02.2021','18.04.2022')
,(1,13,'02.01.2019','02.01.2020')
,(1,12,'01.01.2018','01.01.2019')
,(1,11,'13.02.2017','13.02.2019')
,(2,23,'19.06.2021','18.04.2022')
,(2,22,'01.07.2019','01.07.2020')
,(2,21,'19.01.2019','19.01.2020')
 
Select User_ID
      ,Days = count(DISTINCT dateadd(DAY,N,Start_Date))
 from @YourTable A
 Join ( Select Top 10000 N=Row_Number() Over (Order By (Select NULL)) 
         From master..spt_values n1, master..spt_values n2
      ) B
  On N<=DateDiff(DAY,Start_Date,End_Date)  
 Group By User_ID

--------------------------------------------------------
-- Normally I include Day 0 -- Note N=-1+Row_Number()...
--------------------------------------------------------
Select User_ID
      ,Days = count(DISTINCT dateadd(DAY,N,Start_Date))
 from @YourTable A
 Join ( Select Top 10000 N=-1+Row_Number() Over (Order By (Select NULL)) 
         From master..spt_values n1, master..spt_values n2
      ) B
  On N<=DateDiff(DAY,Start_Date,End_Date)  
 Group By User_ID

User_ID	Days
1	1477
2	832

User_ID	Days
1	1479
2	834