A way to process a CTE once?
There is no query hint to spool or materialize a CTE.  So use a temp table, and optionally index the temp table.
SELECT s.[DTL ID] AS ID, s.[NEW TEU]
into #splits
FROM   [POTS].[vwSPLITCARGO] AS s;

WITH
  splits(ID, [NEW TEU])
  AS
    (select * from #splits)
     
SELECT *
FROM   [MISNT].[CARGO_MANIFEST_DETAIL_VIEW] AS cmd
       LEFT JOIN splits AS s ON s.ID = cmd.ID