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Format SQL to a custom JSON format

I have this query

WITH cte AS (SELECT CenterId, EOMONTH(MIN(Change_date)) AS EOM_Date, EOMONTH(MAX(Change_date)) AS finish
             FROM #tempCenters
             GROUP BY CenterId
             
             UNION ALL 
             
             SELECT CenterId, EOMONTH(DATEADD(MONTH, 1, EOM_Date)), finish
             FROM cte
             WHERE EOM_Date < finish)
             
             
SELECT DISTINCT cte.CenterId, 
       FIRST_VALUE(Members) OVER(PARTITION BY cte.CenterId, cte.EOM_Date ORDER BY tc.Change_date DESC) AS 'EndOfMonthData.Members', 
       cte.EOM_Date AS 'EndOfMonthData.Date'
FROM cte 
LEFT JOIN #tempCenters tc ON cte.CenterId = tc.CenterId AND cte.EOM_Date >= tc.Change_date
ORDER BY cte.CenterId, EOM_Date
FOR JSON PATH, ROOT('data')

which returns this

CenterID Members EOM_Date
1 100 2020-02-29
1 100 2020-03-31
1 130 2020-04-30
1 130 2020-05-31
1 130 2020-06-30
1 130 2020-07-31
1 130 2020-08-31
1 180 2020-09-30
2 200 2020-01-31
2 200 2020-02-29
2 106 2020-03-31
2 106 2020-04-30
2 106 2020-05-31
2 135 2020-06-30

but I need the result as JSON in the following format:

{
  "data": [
    {
      "centerId": 1,
      "EndOfMonthData": {
        "2020-01-30": 100.00,
        "2020-02-28": 100.00,
        "2020-03-31": 130.00
        ...
      }
    },
    {
      "centerId": 2,
      "EndOfMonthData": {
        "2020-01-30": 200.00,
        "2020-02-28": 200.00,
        "2020-03-31": 106.00,
        ...
      }
    }
  ]

But this is the output I've got so far

{
    "data": [
        {
            "CenterId": 1,
            "EndOfMonthData": {
                "Members": 100,
                "Date": "2020-02-29"
            }
        },
        {
            "CenterId": 1,
            "EndOfMonthData": {
                "Members": 100,
                "Date": "2020-03-31"
            }
        },

... ] }

I've tried with the JSON AUTO, JSON PATH with dots, without dots, but nothing close to what I need. Any help will be really appreciated.

SQL Server is declarative by design. You would have to either have to use Dynamic SQL or a little string manipulation.

Example

Declare @table1 Table ([CenterID] int,[Members] int,[EOP_Date] date)
Insert Into @table1 Values 
 (1,100,'2020-02-29')
,(1,100,'2020-03-31')
,(1,130,'2020-05-31')
,(1,130,'2020-06-30')
,(2,200,'2020-01-31')
,(2,200,'2020-02-29')


 SELECT [CenterID]
       ,EndOfMontData  = JSON_QUERY('{'+string_agg(concat('"',EOP_Date,'":',Members),',')  WITHIN GROUP( ORDER BY EOP_Date) +'}')
 FROM   @table1
 Group  By CenterID
 Order By CenterId
 For JSON Path,Root('data')

Results

{
   "data":[
      {
         "CenterID":1,
         "EndOfMontData":{
            "2020-02-29":100,
            "2020-03-31":100,
            "2020-05-31":130,
            "2020-06-30":130
         }
      },
      {
         "CenterID":2,
         "EndOfMontData":{
            "2020-01-31":200,
            "2020-02-29":200
         }
      }
   ]
}

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