Well you named the all-stars, so I'll have to do some digging and give alternative suggestions.

Terraria sounds somewhat close. Think 2D Minecraft but you recruit NPCs that give you bonuses. However it might not be the rat feeling all the time.

Lobotomy Corporation is a base-builder where you manage anomalies SCP style. You are a Power Company that has some, uh, unusual methods for generating electricity. Definitely makes you feel like the rat in the cage sometimes when things go south.

People have recommended Rimworld, Dwarf Fortress, and Frostpunk. I might as well throw Timberborn in the ring. You manage a bunch of highly advanced beavers that construct elaborate machines and dams for water management during droughts. However it isn't a rat-like feeling. Bonus: humans extincted themselves.

The original Homeworld is a 3D RTS has persistent fleets and resources between missions, and you can steal enemy ships including unique AI ships for yourself. Homeworld Cataclysm/Emergence takes this concept and applies survival-horror.

As long as I'm on the weird recommendations, how about an "Unfair" strategy game, AI War: Fleet Command? This is a rat-like experience. The whole game is set up where you are always lethally disadvantaged right up until you win. The AI has overwhelming power, but it doesn't notice you yet. The whole game is about managing a deteriorating ignorance of the AI while you build up enough power to strike at it. There are two of these AIs, and killing one make the other notice and destroy you. The entire game builds up to a climactic battle where you make a desperate strike at both AIs before they can fully muster their forces. I still haven't beaten it yet

Honorable mentions:

• Factorio - Begins as a survival scavenger, but my mid-game you are in full logistics mode. Late game is basically an elaborate RTS. Mitigation: crank up research and construction costs to balloon the early game, deathworld settings make enemies more dangerous and frequent.
• Stardew Valley - Harvest Moon farming sim early game, but mid to late game materials require Dungeon Crawling.