Split string to join to table and rejoin

I have data in a database that I cannot change which is stored like this:

where:

1395/3003 = Cat Stevens/Therapist

and

1399/1388 = Dog Stevens/Program Staff

I only want a concatenated row of the staff names separated by commas like this:

I need to split the ids from the '/' and then join them to a StaffContacts table to get the name. After that, I need to join them again into one row. I am using SQL Server version 13 so cannot use String_Split. I have this so far:

WITH CTE                        
AS                          
  (SELECT                           
  DocId                         
  ,Split.a.value('. ', 'VARCHAR(100)') 'Staff'
   /* Separate into separate columns */                         
  FROM                              
    (SELECT DocId, CAST ('<M>' + REPLACE(Staff, ',', '</M><M>') + '</M>' AS XML) AS Data
     FROM CustomerDocument cd                                               
    ) AS B                      
    CROSS APPLY Data.nodes ('/M') AS Split(a) /* Unpivot into rows so can join to tables below */   
)   


/* Get Staff */                         
(SELECT DISTINCT stafftab.DocId                             
  ,[Staff] = STUFF(/* This is added to delete the leading ', ' */                           
     (SELECT DISTINCT ', '  + ([FirstName]+ ' ' + [LastName])                   
        FROM cte                    
        JOIN Documents d on cte.DocId = d.DocId                 
        JOIN StaffContacts sc ON d.ClientId = sc.ClientId                                   
    WHERE sc.Relationship in (                  
            SELECT CodeId               
            FROM Codes co 
            Where categorycode = 'Staff')       
            AND cte.DocId = stafftab.DocId              
     FOR XML PATH ('')) /* Concatenate multiple rows of data into comma separated values back into one column */                        
     , 1, 2, '')   /* At 1st character, delete 2 which deletes the leading ', ' */                      
         FROM cte stafftab
)

However, I am getting this result:

I tried to include this code in the above since it separates the name from the '/' but I haven't been able to get it to separate successfully to join to the StaffContacts table and then be concatenated again.

SELECT DocId,
LEFT(Staff, charindex('/', Staff)-1)
FROM CustomerDocument cd

Is there another way to do this in the version of SSMS that I have? Thank you.

This should work on SQL Server 2016 with compatibility level 130. If your compatibility level is lower, you will need to use some user-defined way to split your strings, I suggest Jeff Moden's CSV Splitter

First, create and populate sample tables (Please save us this step in your future questions):

CREATE TABLE CustomerDocument (
    DocId INT PRIMARY KEY,
    StaffRelationship NVARCHAR(MAX)
);

INSERT INTO CustomerDocument (DocId, StaffRelationship)
VALUES (127866, '1395/3003,1399/1388');


CREATE TABLE Staff
(
    id int,
    name nvarchar(100)
);

INSERT INTO Staff (id, name) VALUES (1395, 'Cat Stevens'), (1399, 'Dog Stevens');

Then, use a CTE combined with STRING_SPLIT and a couple of CROSS APPLIES to get your data in a normalized way, and then use a combination of STUFF and FOR XML PATH to aggregate the strings back together. (unfortunately, STRING_AGG is only available from 2017 version)

WITH CTE AS (
SELECT docid, staffId
FROM CustomerDocument
CROSS APPLY (SELECT * FROM STRING_SPLIT(StaffRelationship, ',', 1)) AS pairs
CROSS APPLY (SELECT value as staffId FROM STRING_SPLIT(pairs.value, '/', 1) WHERE ordinal = 1) AS singles
)

SELECT DISTINCT docid, STUFF
    (
        (
          SELECT ', ' + [name]
          FROM CTE
          INNER JOIN Staff
          ON staffId = id
          FOR XML PATH('')
        )
    , 1, 1, '') AS Staff
FROM CTE 

Results: