Still fairly old, but newer than B&W: From Dust . Replace trainable animals with fluid physics and light hearted songs with didgeridoos, and it’s kind of similar.
DREDGE is great, and does overlap with Sunless Seas in some ways, but is nowhere near as story driven (or weird). That said, it’s a lot easier/more forgiving, and has a simpler (and potentially more engaging) main gameplay loop.
I love the Sunless/Fallen London setting, and really wish Seas had some of the improvements of Skies, as I think I prefer the setting of Seas, but I’ve found it hard to go back to, having played Skies.
This might not be exactly what you’re looking for (as it can be a little rogue-like), but it’s a game that when I looked for similar things, led me to Dredge: Sunless Sea
You’re a ship captain trying to survive in Victorian era London, after London was stolen by bats and taken to the shores of the Unterzee, an underground sea filled with some very strange creatures, people and locations. This means exploring and finding new trade routes or ways to survive while uncovering the stories of the islands you find, those of your crew, and the larger world.
There’s a sequel, Sunless Skies, where you command a space going train exploring the heavens. It’s a bit easier and has some good quality of life improvements, but I prefer the setting of Seas.