As you say: depreciation is added back because there is no cash flow.
That’s not the reason that interest is added back, because there is cash flow with interest.
Paying interest is a _ use _ of FCFF. If the firm chooses to use the cash to pay interest, it gets a tax break. If the firm chooses to use the cash for something else, it might not get the tax break. The idea of calculating FCFF is to arrive at the amount of cash available before that decision is made; before that decision is made the firm hasn’t paid interest (so add back 100% of interest), and the firm hasn’t received the tax break from paying interest (so subtract the tax saving).