Excel Formula

The problem is that you are doing an average of averages which is NOT correct. 

Basically if you have the number 1,2,3,4,5,6,7,8,9 the average is 5 but if you do the average of 1,2,3 it is 2 and the average of 4,5,6,7,8,9 is 6.5 and then the average of 2 and 6.5 is 4.25 NOT 5

In your M3 formula you want to do a SUM and SUMIFS instead of the AVERAGE and AVERAGEIFS and then divide by the number of days (ed-sd+1).

That said you have another item I should point out: 

You are using the EDATE formula to determine 1 month later but EDATE(...,1) of a day > than the next month total days is the last day of that month so EDATE('2025-01-31',1) is 2025-02-28.  so that "month" range would only be from 2025-01-31 to 2025-02-27.  

I'm also not a fan of the MAP and INDIRECT but not sure of a 'simple' alternative.