Compare Two list and sum values based on all matching values and by month

Try

in C10

=SUMIFS(Data!$E$2:$E$34,Data!$A$2:$A$34,Summary!C$8,Data!$D$2:$D$34,Summary!$A10)

Copy across and down

I interpreted a little differently. I understood you want to include all the items in Summary!$A:$A and include even if they are only part of the strings in Data!$D:$D

And since you want to also include any additions (automatically?) they are referenced by a dynamic range $A$10:INDEX($A:$A,MATCH("zzzz",$A:$A)) embedded in the formula. It's a bit awkward so I would recommend saving that bit as a dynamic named range (DNR) in Name Manager and reference it by name in your final formula(s).

Try this in the meantime.

Formula:

=SUM(SUMIFS(Data!$E:$E,Data!$D:$D,"*"&$A$10:INDEX($A:$A,MATCH("zzzz",$A:$A))&"*",Data!$A:$A,Summary!C$8))

With that DNR as Element_Names this formula is shorter.

Formula:

=SUM(SUMIFS(Data!$E:$E,Data!$D:$D,"*"&Element_Names&"*",Data!$A:$A,Summary!C$8))