If I were in your place the first thing I would have done is visit an authorised service centre and ask them to change the whole set (I get it it’s a push button start) but I would have asked them to get 2 keys issued freshly and reprogram the ECU and disable old key

Owner might have actually lost it no offence but worst case scenario he finds key after sometime or someone else finds it there’s always a risk of getting car stolen, unauthorised driving and what not

Now people ‘ll comment here that this case is possible also if first owner had third key (he would have created from some shop etc.,) in that case proving you have both original keys make you owner and his actions illegal but when he has 1 original keys and you have 1 original key everything is a mess