Civ I’d say (while relatively simple in most versions) is very much on the strategy side. While maneuvering units in the battle theater matters, wars are mostly won or lost by the tech and economics and diplomatic situation going in, and the timing of the decisions to start and end the war.
Civ5 and Civ6 has moved more tactical. I'm spending more and more time thinking about where to place units, because they no longer "stack up" with each other. Collision detection for the human means that I need to put more effort into deciding where to move and place my units.
Yeah yeah yeah, people were confused about "stack kills" in Civ1/2/3, and without stack-kills, Civ4 combat grew dull. So maybe removing stacks all together was a solution (the current direction for Civ5 and Civ6).
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Somewhere along the line, combat was no longer a guaranteed killer. (Civ1/2 was definitely a "win you live, lose you die" for every combat). Civ6, now I'm thinking about movement points, where to retreat to, how to save up HP again and recover, whether or not I can cutoff the opponent's retreat. These are more tactical elements.
I feel like Civ6 has pushed "strategy" through its government card system, which is pretty abstract (Oh, you just got a new government card! Time for a new war! I'm going to equip +100% pillage bonus and +4 Strength bonus). A lot of Civ6 is about abusing the multiplicative bonuses of these cards at the right timing.
Wargroove's AI is a bit dumb compared to Adv. War's Days of Ruin however. The game really shines as a competitive player-vs-player setting. But if you're not used to the mechanics of Adv. Wars, you probably need the easier AI to learn how quirks of Adv. Wars style / Wargroove style play.
Nintendo is remaking Advance Wars 1 and Advance Wars 2 ("Reboot Camp") for the Switch. I'll be revisiting these originals-remakes as they come out in a few months. I remember the CO-powers being incredibly overpowering (while Wargroove's special "grooves" are quite powerful as they are, they are no where on the level of CO-powers or CO-superpowers of the original).
Civilization is on the easier / simpler end of 4X / Strategy... and believe me, this is a good thing!! Things get really complicated. Paradox games (Victoria, Hearts of Iron, Crusader Kings, Europa Universialis) are the "complicated" games, technically realtime but the underlying simulations "feel" turnbased. (Hearts of Iron progresses the simulation in 1-hour increments. They're "realtime" only because it'd be too boring to hit "next turn" so often, but you can hit the pause button and really think about a situation at say: September 1st 1939 @ 1pm if something terrible is going on)
Romance of the Three Kingdoms is also a strategy game: war, tactics, resources, diplomacy, etc. etc. The elements you'd expect.
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"Tactics" games that focus on a singular battle as the core gameplay loop. Fire Emblem, Wesnoth, Wargroove, Advance Wars, Heroes of Might and Magic, Panzer General, Starcraft, Age of Empires.
"Strategy" games approximate the battles and focus on larger scale elements.
A good rule of thumb is that Strategy Games have an element of siege and supply lines, while Tactics games often just "teleport" the resources where needed. Tactics are about maneuvering your troops to get an advantage, Strategy is about finding / securing resources (ex: placing your defensive Pikeman on the enemy's mine in Civ2, or in their districts in Civ6)
Civ leans towards the simpler/tactics side, but is just barely enough "Strategy" that I'd group it in the strategy side of things.