How do I know us savings bond interest is excluded from my state taxable income. Where do I look to verify that it was automatically excluded?

When you enter the 1099-INT in Federal > Wages and Income > Interest, there is a question that asks if it is US Treasury interest that requires special state handling.

On your State tax return, some states post it as an adjustment, while others just omit it altogether.

It will depend on the state, but there should be a worksheet or form documenting the exclusion.