without set up scripts of r create table / insert data....here is a guess

WITH cte_st

AS (

SELECT

S.GroupID

, MIN(ST.StatusID) AS minst

FROM StepTable AS S INNER JOIN

StatusTable AS ST ON S.StatusName = ST.StatusName

GROUP BY

S.GroupID)

SELECT

S.ID

, S.StepID

, S.GroupID

, S.StatusName

, ST.StatusName AS NewStatus

FROM StepTable AS S INNER JOIN

cte_st ON S.GroupID = cte_st.GroupID

INNER JOIN

StatusTable AS ST ON cte_st.minst = ST.StatusID

ORDER BY

S.ID;