This is a weird one, because I think the title of the game is putting people off as it's nowhere near as popular as it should be. However, please give me a chance here to convince you to try it.
Intergalactic Fishing.
You don't actually need to be into fishing games to enjoy it. The fishing, although about as addictive as most good fishing minigames, is only a small portion of the game.
It also revolves around a similar style of exploration to some space games, such as No Man's Sky and Elite Dangerous. While progressing through the storyline you will gain access to undiscovered lakes with their own unique species of fish, and information collected about these lakes can be sold.
Catching fish gives you information about that fish's likes in terms of lure, along with a few other attributes. You can then use this information to design a lure to suit it. This becomes a puzzle game, as lures are designed by arranging squares on a grid. Factors such as "shininess" and "noise" are infkuenced by putting more blocks near the edges, or leaving more holes and forming irregular shapes.
It's primarily a sandbox game, but there is a short storyline. Once finished though, the game opens up into an addictive endgame that I don't want to spoil. Tournaments and contracts are a nice diversion throughout the game and can also net you (sorry for the pun, but fish puns are hard to avoid) a decent amount of cash.
It's quickly become one of my favourite games of all time.
Hey again, you'll probably need a minute to remember making this post, but I saw Intergalactic Fishing was on sale in the Steam Summer Sale, so I went ahead and bought a copy. This lives up to everything you've said - I very much enjoy the gameplay of messing with the lure puzzle minigame and collecting information on all the fish in any given lake, and I'm absolutely wanting to catch Just One More Fish.