how do i get this average percentage formula to work across multiple sheets?

try in B2 of stats sheet if A2:A contains dates:

=ARRAYFORMULA(IFNA(VLOOKUP(A2:A, 
 QUERY({SHEET01!A2:B; SHEET02!A2:B; SHEET03!A2:B}, 
 "select Col1,avg(Col2) 
  where Col1 is not null 
  group by Col1 
  label avg(Col2)''"), 2, 0)))

or use only this to get the full summary:

=QUERY({SHEET01!A2:B; SHEET02!A2:B; SHEET03!A2:B}, 
 "select Col1,avg(Col2) 
  where Col1 is not null 
  group by Col1 
  label avg(Col2)''")

note that you might need to format dates via 123... button if your dates will outputted as 4000+ numbers

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