United are happy to take some pressure off their wage bill, hence the discount, he didn't fit into Amorim's scheme anyway so it's a win-win move. It will be interesting to see how he will do at Chelsea, he was once considered a very promising player. Chelsea are on the rise now and I wouldn't be surprised if this gives a good boost to his career. And yes, I think he improved his salary conditions, otherwise why would he sign such a long-term contract - 7 years is a lot.
I have come to understand that players does better when they are around other quality players and most times they improve significantly, just look at Pedro Neto at Chelsea, he has improved significantly just by playing around more quality players, so I believe that garnacho is a steal for the @£40m he was bought., and he is more likely to improve more in the colors of Chelsea.
As for the long contract given to him, I really don't sees it as an obstacle because if he does well, along the line they might improve his contract just like they did to cole palmer, but if he did not do well , he will be sold easily just like Nicholas Jackson and the rest of other players that are having long term contract but were still sold.