Are you sure it's a 145.005 (cal 321), and not a 145.018 (cal 861) - there are two references that share a similar case, and similar dials - some badged as De Ville, some as Seamaster.
Movement pictures and inside of case back would be helpful to work out what you actually have here.
If it is a 145.005,
as far as I'm aware, it should have a dial that reads (top to bottom) - Omega, Seamaster, DE VILLE.
If it's a 145.018,
again as far as I am aware, it can either be a Seamaster, or a Deville.
So if this is a 145.005, it
may have a later replacement dial on.
Pushers, as you point out, are not a matched pair.
Realistically, you need pictures of the insides to make a fair assessment of this (or any other) watch.
Equally, if you go have a good research of both 145.005, and 145.018 - you'll have a better idea of what these watches should be like, and be able to use that knowledge to reference against a piece that you want to buy.