Adding data from template into program rollup sheet

I am hoping this is an easy solution, but Id like to automatically add data from a "template" into my program rollup sheet. That is, when a user uses the "Project Budget" template, Id like to automatically copy portions of the data from that new budget and have it copied into another sheet (where my program roll-up data is housed). I cant figure out a way to do this automatically and am unsure if I bake those formulas into a template if it'll work as more templates are used).

When a new budget template is used, shown below, I want to copy that data to be shown in corresponding columns on my overall tracker.

Budget template:

Program Roll-Up:


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