How to update group no incremental by 1 based on every group from 1 to 3?
Check if it works for you. Please, notice this code is meant to work with groups containing no more than 3 steps each.
;WITH CTE_Replacement
AS
(
    --Creates the groups by selecting only the rows with step 1
    SELECT PartIDC, 
        PartIDX, 
        FlagStatus, 
        HasReplacement, 
        ROW_NUMBER() OVER(ORDER BY PartIDC) AS groupId, 
        step
    FROM #Replacement
    WHERE step = 1

    UNION ALL

    --Gets steps 2 that are lelated to the groups with step 1 from the query above
    SELECT R.PartIDC, 
        R.PartIDX, 
        R.FlagStatus, 
        R.HasReplacement, 
        CTE.groupId, --Uses the group created before
        R.step
    FROM #Replacement R
        INNER JOIN CTE_Replacement CTE ON R.PartIDC = CTE.PartIDX
    WHERE R.step = 2
) 
--Adds the last step of each goup
SELECT R.PartIDC, 
        R.PartIDX, 
        R.FlagStatus, 
        R.HasReplacement, 
        CTE.groupId, 
        R.step 
FROM #Replacement R
    LEFT JOIN CTE_Replacement CTE ON R.PartIDX = CTE.PartIDX
ORDER BY CTE.groupId, CTE.step;