The center to center distance between screws is 2 3/8". I remeasured the width and I believe your width of 2 9/16 is correct. The depth at the widest part is 1 1/8 and the depth where the screws by the latch lever is 1/2.
Tom from SWISCO responded:
May 18, 2020
Your old lock isn't made anymore, but you can use our 38-097 and 38-098 as a substitute. These won't be compatible with your old keeper, though, so you'll also need a new 38-079.