Need total sum of hours for each shift assigned to each taks and team

It would be better if you kept the same formats through-out.
- Keep dates as dates...yours are text that looks like at date - not a big deal right now, but will cause problems if you want to start summaries by date
- Keep times as times...you have real times on Template, but text that looks like time on Data

It is always good practice to keep to the correct formats, otherwise formulas become complex trying to convert or accommodate mixed formats.

I changed the "times" on Data sheet to be real times.
Then on Template in B3, copied down, use this...
=SUMPRODUCT((Data!$G2:$BB224)*(Data!$G$2:$BB$2>=Template!B$1)*((Data!$G$2:$BB$2<Template!D$1)*(Data!$C2:$C224=Template!$A3)*(Data!$B2:$B224<>"TEAMD")))
You can copy this to all the "other team" columns as well.

For the Team D columns, use this...
=SUMPRODUCT((Data!$G2:$BB224)*(Data!$G$2:$BB$2>=Template!B$1)*((Data!$G$2:$BB$2<Template!D$1)*(Data!$C2:$C224=Template!$A3)*(Data!$B2:$B224="TEAMD")))

Sorry for the delay in getting back tou you. See the arttached

yuppers, the devil is in the detail, as they say Thanks for the feedback

Try in D3:

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...confirmed by pressing CTRL+SHIFT+ENTER to activate the array, not just ENTER. You will know the array is active when you see curly braces { } appear around your formula. If you do not CTRL+SHIFT+ENTER you will get an error or a clearly incorrect answer. Press F2 on that cell and try again.

Note that as with SUBTOTAL in formula, to get displaying results in sheet 'Template' make sure not to filter task column in sheet Data.
For instant, task 1 in sheet 'Template' would displays 0 if filter for other task in sheet 'Data" is activated