Append Tables as New No Duplicates Three Unique Columns

This should work but only if you do it exactly in this order and if those three columns are truly your primary key.

= Table.Distinct(DailyMonth & ShippedDel24 & ShippedDel23 , {"Delivery", "Material", "Item"})

Also, for some reason when I append my Queries as New it duplicates two of my columns and enters a null value in each row for those two columns.

Power Query is case sensitive.  You have spelling differences or trailing spaces.

all my column headings are the same

I would respectfully like to challenge you on that. If Power Query produces extra columns then there must be differences.  Please show all column headers in their natural habitat.