People often have multiple motives for an action. If banks pay interest on deposits and make them redeemable on demand at par for cash, then customers can hold deposit balances for both reasons. It’s not necessary to separate their motives in order to compute the funds devoted to saving-investing and the funds devoted to money holdings.
One can determine the extent of saving-investing in the economy by adding up all the funds spent on producers goods. The sources of saving-investing can be determined by adding up self financed funds and financed funds. Banks contribution to the later can be discovered by looking at their loan portfolios on the asset side of their balance sheets.
One can determine the money stock in the economy by adding up all money proper plus all money substitutes, i.e., all redemption claims to money payable on demand at par.