Do I need to enter “total expenses” or “cost of goods sold” anywhere in the tool?

You are "spot on" - no need to enter any other specific expenses as "net income" for a pass through entity is pretax income for the individual owners, i.e. the net income result accounts for the deduction of ALL relevant expenses.

Likewise, you do not need to enter “total equity” due to the fact that you have already entered data which accounts for “All Assets” and “All Liabilities”, i.e. the accounting equation holds that:

Total Assets minus Total Liabilities equals Total Equity

And

Total Liabilities plus Total Equity equals Total Assets