Variable Cell Value Format In Query Function - google-sheets

Question

I know "Format" can be used in a Query function (i.e Query(A1:G2,"Select * Format C 'MM/DD/YYY'")) but I'm stuck on how to use it in my more complicated query. Essentially I want all the selected Columns to be formatted to dates "MM/DD/YYYY", but I can't do it in the cell itself because this query is part of a variable query function that pulls data based on a user input, and only THESE column pulls are in date formats, all the other pulls are plain numbers or text. I tried putting the Format in myself but it never works or the output gives me the IfError False readout of "No Matches Found". Can anyone assist?
IFERROR(QUERY({Training!A3:AP},"select Col3,Col4,Col5,Col6,Col7,Col8,Col9,Col10,Col11,Col12,Col13,Col14,Col15,Col16,Col17,Col18,Col19,Col20,Col21,Col22,Col23,Col24,Col25,Col26,Col27,Col28,Col29,Col30,Col31,Col32,Col33,Col34,Col35,Col36,Col37,Col38,Col39,Col40,Col41,Col42 where "&TEXTJOIN(" and ", 1, IF(Lower(B3)<>"", "Lower(Col1) contains '"&Lower(B3)&"'", ),IF(Lower(B4)<>"", "Lower(Col2) contains '"&Lower(B4)&"'", ),If(Lower(B5)<>"", "Lower(Col6) contains '"&Lower(B5)&"'", ),IF(Lower(B7)<>"", "Lower(Col9) contains '"&Lower(B7)&"'", ),If(B6<>"",Vlookup(B6,Classes!G2:H,2,False)&" contains '"&B6&"'",),), 0), "No Matches Found")))

Answer 1

format in QUERY is buggy. use this:
=ARRAYFORMULA(IF(B2="", "Please Select Criteria",
IF(B2="Licenses", IFERROR(QUERY({Licensing!A3:D,
IF(Licensing!E3:E="",,TEXT(Licensing!E3:E, "dd/mm/yyyy")), Licensing!F3:F,
IF(Licensing!G3:G="",,TEXT(Licensing!G3:G, "dd/mm/yyyy")), Licensing!H3:H,
IF((Licensing!I3:AQ<>"")*(MOD(COLUMN(I3:AQ)+1, 4)=0),
TEXT(Licensing!I3:AQ, "dd/mm/yyyy"), Licensing!I3:AQ)},
"select "&JOIN(",", "Col"&ROW(3:7), "Col"&FILTER(ROW(9:43), NOT(MOD(ROW(9:43), 4)=0)))&"
where "&TEXTJOIN(" and ", 1, "1=1",
IF(LOWER(B3)="",,"lower(Col1) contains '"&LOWER(B3)&"'"),
IF(LOWER(B4)="",,"lower(Col2) contains '"&LOWER(B4)&"'"),
IF(LOWER(B5)="",,"lower(Col6) contains '"&LOWER(B5)&"'"),
IF(LOWER(B7)="",,"lower(Col10) contains '"&LOWER(B7)&"'"),
IF(B6="",,"Col"&MATCH(B6, Licensing!2:2, 0)&" is not null")), 0), "No Matches Found"),
IFERROR(QUERY({Training!A3:D,
IF(Training!E3:E="",, TEXT(Training!E3:E, "dd/mm/yyyy")), Training!F3:F,
IF(Training!G3:AP="",,TEXT(Training!G3:AP, "dd/mm/yyyy"))},
"select "&JOIN(",", "Col"&ROW(3:42))&"
where "&TEXTJOIN(" and ", 1, "1=1",
IF(LOWER(B3)="",,"lower(Col1) contains '"&LOWER(B3)&"'"),
IF(LOWER(B4)="",,"lower(Col2) contains '"&LOWER(B4)&"'"),
IF(LOWER(B5)="",,"lower(Col6) contains '"&LOWER(B5)&"'"),
IF(B6="",,"Col"&MATCH(B6, Training!2:2, 0)&" is not null")), 0), "No Matches Found"))))

Answer 2

This may not help, but I believe the issue is that the FORMAT clause in the QUERY function does not override the cell format in the output area. I did some testing, and found that with the following simplified version of your formula, I could get the format of the output to change, for example from 'mm/dd/yyyy' to 'yyyy-mm-dd'.
"select Col3,Col4,Col5,Col6,Col7,Col8,Col9,Col10,Col11
where "&TEXTJOIN(" and ", 1,
IF(Lower(B3)<>"", "Lower(Col1) contains '"&Lower(B3)&"'", ),
IF(Lower(B4)<>"", "Lower(Col2) contains '"&Lower(B4)&"'", ),
If(Lower(B5)<>"", "Lower(Col6) contains '"&Lower(B5)&"'", ),
IF(Lower(B7)<>"", "Lower(Col9) contains '"&Lower(B7)&"'", ),
If(B6<>"",Vlookup(B6,Classes!G2:H,2,False)&" contains '"&B6&"'",),
) & " Format Col9 'dd-yyyy-mm', Col11 'dd-yyyy-mm' ", 0)
But this only worked if the cell/column was formatted as Automatic. And worse, I can't reliably reproduce the behaviour yet. On another copy of the sheet, it won't change the format.
Anyway, if you want to see it working, here is a link to the cell in my copy of your sheet.
Maybe someone else will have a clearer explanation of the issue and how to address it.