Yes I think the story behind the missing engine would be most definitely worth establishing
At a stretch it might be something charitable like they sent it for an OH to some cowboy who ran off with it...
I also see the belly panels are missing, which is bizzare.
Re what to do with it, I was not thinking of selling the finished thing. One would never make a profit. For an an owner though, it would make sense because if you rebuild a plane in that way, you know what is in it and you are not inheriting some can of worms. Many if not most people sell a plane because they are fed up with regular issues causing downtime and hassle.
And if one wanted a major avionics refit (I mean well into 5 digits) it makes more sense to do it on a wreck (but whose metalwork is in good condition) than on a plane which already contains a load of good avionics which will need to be ripped out and which will never sell at a meaningful price. The other reason it makes sense is because the job will take months - even if you can find an avionics shop which can spell "project management" which is a rarity.
A TB20GT is an excellent and for the most part very well engineered long range tourer - even if I am biased
