Why is common stock included in bank capital?
Equity/stock/capital does absorb losses. Here is a stylized example:

Ann creates a new bank. She puts in \$100 of her own money. This \$100 is her equity/stock/capital.

She borrows another \$900 (debt). (For simplicity we'll assume that all debt/loans have an interest rate of 0%.)

She has a total of \$1,000. She lends all of it to Bob.

A little later, Bob is able to repay only \$925. So, \$75 was lost on this loan.

This \$75 loss is entirely absorbed by the equity/stock/capital, which now falls from \$100 to \$25.