Excel: Proportional monthly distribution of sample values over a time period spanning different months

I am trying to get my head around an MS excel formula for a scenario I have.

I am recording discharges over various sample periods. These sample periods will last anywhere from 24 hrs to 1 week. The sample period will be recorded with a start and end time (dd/mm/yy hh:mm).

I want to be able to report the sum discharge total for all sample periods for each calendar month, but ensuring that any sample periods that span two months (i.e. 27/02/24 14:00 >> 05/03/24 14:00) have the total discharge value proportionately distributed between each month total. I acknowledge that this assumes that the discharges are constant rate, which they are for this task. For the time range in brackets, this would be ~34% of the sample period total allocated to Feb-24 as an example.

If anyone can suggest a formula for F3 to satisfy what I've described above, that would be fantastic.

Screenshot attached.

Screenshot

I haven't tried anything so far, because I don't really know where to start with this. I've tried in vain to find a solution online.

You can use the overlap formula

Min(startTime1,startTime2)-max(endTime1,endTime2)

to give you the number of days and hours which fall within the current month. When applied as an array formula in this case it would give you

=LET(dis,C$2:C$4,
startDis,A$2:A$4,
endDis,B$2:B$4,
startMonth,E2,
endMonth,EOMONTH(E2,0)+1,
overlap,IF(endMonth<endDis,endMonth,endDis)-IF(startMonth>startDis,startMonth,startDis),
posOverlap,IF(overlap<0,0,overlap),
SUM(posOverlap*dis/(endDis-startDis)))

Note the use of eomonth(E2,0)+1 which takes you to midnight on the last day of the current month.