I have a few ideas.
The first one that I recommend is Bad North. It's a real-time tactics game where you command squads of vikings in order to defend various islands from invaders. As you complete islands, you get money which can be used to upgrade your units and specialize them into one of 3 classes, as well as purchase more general stat upgrades as well as items and abilities. You also gain more units as you play increasing the complexity of the battles you participate in. When you say you want a game with "narrative", I assume you don't mean it in a literal storytelling sense and really just want a game with "progression". Where the battles you engage in late-game are meaningfully different from the stuff you do early-game. I think this game does a good job of fulfilling that goal as your units gain more abilities and as the enemy types become more challenging and interesting.
If you aren't sold on this yet, I would recommend looking up some gameplay. In my opinion, its a simple and satisfying core loop is one that anybody can enjoy even if it isn't exactly what you're looking for.
I'd also like to recommend XCOM, FTL, and Battletech. I don't have the time to write paragraphs for these games like I did for Bad North, but I'll try to give very short summaries. The XCOM franchise is one of the best turn-based tactics games ever made. In each mission, you command a squad of 4-6 soldiers and accomplish objectives (usually some form of killing aliens). As soldiers complete missions, they will level up and acquire new skills and each new skill adds a powerful new option for how to use that soldier. It's hard to understate how amazing the skill system is in this game! It's a classic for a reason. I recommend starting right from the sequel assuming your computer can run it.
FTL is a game about piloting a spaceship through a hostile solar system in order to face off a big and dangerous final boss, acquiring upgrades along the way. This includes things like obtaining new weapons, new crew (though they aren't as interesting as XCOM's), as well as special augments that help tweak your ship in a certain way. There are also numerical stat increases, but what prevents them from being boring is that the choosing which stat to upgrade is a very tricky and meaningful choice that demands a lot of thought. Sure you could upgrade your ship's shields, but then you might not have enough currency by the fancy new weapon or hacking system you might encounter in the next shop. But you'll have to upgrade those shields eventually though.
Battletech is not as big as those two games I mentioned above, but it's probably the closest to what you want even though I don't think it is as good (still a fun time though, just not a masterpiece like those other two). You start with a squad of 4 mechs, and you will pilot a squad of 4 mechs for the entire rest of the game. Progression comes in the form of leveling up your crew (whose abilities aren't that interesting), but more importantly acquiring new mechs and the weapons to arm them. Now mech progression goes a long way. You start off with 25 tonne "light" mechs and you will eventually be able to work yourself up to 150 tonne "Assault mechs". There are almost a hundred different mech chassis and each one is highly customizable. The core gameplay isn't as refined as XCOM's, but I get the feeling that you've already played XCOM.