I agree that an OAK is a good idea. Keep in mind that the older Austroflamm Integra air inlet pipe where the air flow sensor is located is not hard piped to the OAK connection on the back of the insert. There is a sizeable gap. This would allow an OAK to be helpful if the house is under negative pressure.
Sorry but I have to wave the BS flag on a stove depleting oxygen levels inside your house. Can't happen. The stove sucks air into it, not just oxygen. Air contains nitrogen, oxygen, CO2, etc. The fire consumes some of the oxygen during combustion, and exhausts through the flue what it pulled in (air) minus some of the oxygen used for combustion, plus combustion by-products (CO, CO2, H2O, etc). It does not selectively suck the oxygen from the room. The air that the stove uses has to come from somewhere. It either comes through your OAK or it comes through cracks or gaps in your houses exterior, windows, doors, etc. The oxygen content of the air in your house will not change unless you have an open fire in the middle of you living room. In that case, it's time to leave. Unless your flue is exhausting into your house, you have nothing to worry about.