I'm glad you asked, because I have opinions LMAO.
I like to think that part of the reason Engi replaced his hand with the gunslinger is because of the fallibility of his human hand.
Mostly because I have carpel tunnel from drawing so much and often think that a robot hand would be more convenient LMAO. I think if people were to ask him, he would give them a blasé, practical answer like that.

But also, the blurb implies that a larger part of this is out of reverence for his grandfather.
We don't get to see Engi interact directly with his dad or grandpa much, other than the time the TFC mercs fight the TF2 ones in the comics I guess. There are some pictures of younger Dell with his dad looking happy and stuff. But I also get the impression that maybe there is a lot of pressure that comes with having a dad like that. I'm certain there's some kind of baggage that comes with being a Conagher, considering their willingness to fight each other. And fatherly baggage seems to be kind of a theme in TF2, huh? LMAO.
I actually have this idea that The Engineer's fatherly affectation comes from a subconscious wish to be more like his dad. He doesn't have any children or a family, far as we know, so it's interesting that he is always pushed as a fatherly figure.
He acts especially fatherly to Pyro, but Pyro is probably around the same age as him, so it's sort of funny. The people around him might find it condescending, even.

He's also willing to fight/even kill his dad, though. It makes me think that maybe, as a kid, Engi held a lot of reverence for his dad and grandpa. But when he grew older, he found out more about them that made him embittered towards them. Maybe being an engineer for Mann co wasn't what he thought it was growing up. Maybe instead of reverence, it's more like competitiveness, and when he calls his grandfather "brilliant" there's a bitter edge to it. But who knows, I mostly just made that up