Matching contents of a cell to comma-separated values in another cell

This formula searches the payee items in column A.
Place it in B2 cell and drag down.
=LET(pay,TRIM(TEXTSPLIT(TEXTJOIN(",",TRUE,SUBSTITUTE(D$2:D$13,",","ß"&RIGHT("0000"&ROW(D$2:D$13),5)&",")),",",,TRUE)), IFERROR(INDEX(C$1:C$13,TEXTJOIN("",FALSE,IF(IFERROR(SEARCH(LEFT(pay,LEN(pay)-6),A2),0)>0,RIGHT(pay,5),"")),0),""))

The row pointer separator not necessary can be left out.

=LET(pay,TRIM(TEXTSPLIT(TEXTJOIN(",",TRUE,SUBSTITUTE(D$2:D$13,",",RIGHT("0000"&ROW(D$2:D$13),5)&",")),",",,TRUE)), IFERROR(INDEX(C$1:C$13,TEXTJOIN("",FALSE,IF(IFERROR(SEARCH(LEFT(pay,LEN(pay)-5),A2),0)>0,RIGHT(pay,5),"")),0),""))

Excel has a fuzzy lookup add-in, but Power Query is built-in and has fuzzy matching options.

To use Power Query

• Put your data into two tables (and name them appropriately)

keyTable

merchantTable

• Select a cell in one table and read it into PQ Data => Get and Transform => from Table/Range

• Then Close and Load To and select Connection Only

• Repeat for the other table.

• in the PQ interface, selet the keyTable query, then Home=>Advanced Editor and paste the code below into the window that opens. (If you have named the tables as I showed, you won't need to change anything)
  Read the code comments for information as to the algorithm.

let
    Source = Excel.CurrentWorkbook(){[Name="keyTable"]}[Content],
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"EXPENSE CATEGORIES", type text}, {"PAYEE", type text}}),

//Need to trim of any trailing or leading spaces or commas
//  and replace and `comma-space` with `comma` only.
//  Then split on the commas and expand the table.
    #"Split Payees" = Table.TransformColumns(#"Changed Type",
        {"PAYEE", (p)=> if p = null then null
            else let 
                    p = Text.Trim(p,{","," "}),
                    q = Text.Replace(p,", ",",")
            in Text.Split(q,","), type {text}}),
    #"Expanded PAYEE" = Table.ExpandListColumn(#"Split Payees", "PAYEE"),

//remove categories that do not have any matching merchants.
//This will make the fuzzy matching more reliable.
    #"Filtered Rows" = Table.SelectRows(#"Expanded PAYEE", each ([PAYEE] <> null))
in
    #"Filtered Rows"

The result should look like:

• Right click in the Queries pane and select New Query - Other Sources - Blank Query
• With that query selected, open the Advanced Editor and paste the code below into the window that opens:
  (Note the Threshold parameter. This is a trial and error thing and 0.60 seems to work best for your data as posted, but you may need to adjust it
  

let
    Source = Table.FuzzyNestedJoin(
                merchantTable, {"Merchants"}, 
                keyTable, {"PAYEE"}, "keyTable", 
                JoinKind.LeftOuter, 
                [IgnoreCase=true, IgnoreSpace=true, Threshold=.60]),
                
    #"Expanded keyTable" = Table.ExpandTableColumn(Source, "keyTable", {"EXPENSE CATEGORIES"})
in
    #"Expanded keyTable"

Result

Note: The merged query can be created from the UI, but it is more difficult to describe the method in this answer.