Our bank has recently set up an affiliate foundation which we intend on making donations to various community needs through...would our bank still receive CRA credit for those eligible donations as if they were made directly by the bank?

if your bank is the only funder of the foundation, and your bank staff invite the organizations to apply for grants, certainly -

You must have a bright line though that the existence of any current or the promise of any potential business relationships with your bank does not influence grant decisions. The bank and the foundation must decline any tangible benefits a grant recipient may decide to give your bank as a result of a grant. There should be no self-dealing.