Effect of buybacks on FCFE

Hi, I get the point that Share Buybacks should not affect FCFE/FCFF as those cash flow measures are supposed to measure the amount which can be used by debt holders+shareholders or in the case of FCFE shareholders only. Therefore, e.g. any dividends or buybacks are not reflected.

However, what if a share repurchase is financed by debt? Shouldn’t the increase in debt increase my net borrowings and, therefore, increase my FCFE? What am I overlooking?

Thanks in advance!