Actual accounting software is double entry. You’ll move that invoice through AP, and the balancing transactions will be split by project/type/etc by a combination of accounts and perhaps labels/tags.
that’s not true. Serious accounting software let you assign an invoice to a project, program, cost center, groups… you can even do that on at the invoice item level.
Actual accounting software can certainly care about that. This is called operational or cost accounting (vs financial accounting, which would be accounts payable etc.)