Is there a game genre that fits this kind of playstyle?

Black and White games! god like games where you slowly n surely build up your towns \ villages with huge populations of people (100s is a lot in the first game, 1000s in the 2nd) and 99.9% its slow paced so the enemy ai barely rarely attacks you until like the last few stages

what about fast paced RTS games like starcraft, command and conquer? if so
theres several free online multiplayer command and conquers
OPENRA - the one i use almost everyday, comes with Dune 2000, CnC95, CnC Red Alert 1
CnCNet dot Org - has more games. havent used in year+ though

browser based one (although its pay to win most of the time)
Travian used to play it for yearssss. for me now that i think of it. super waste of time.
starting off in the game its typical tiny village = a few minutes of gameplay a day at most. the larger you build yourself up the more of a time sink it becomes. and you may end up setting up alarms for when the next unit \ building is produced\upgraded many hours later so you can do your next action that takes many hours.

there is of course several 3x speed, speedier servers for travian too.

There have been a lot of good suggestions of games to play (Disgaea is a top pick for grinding, also try Phantom Brave on Steam for more grinding and wacky hijinks) so I'm mainly posting to say that SRPGs (Strategy RPGs) in general would categorize in one genre what you are looking for.
Most games in that genre contain a good level of grinding for resources or levels to maximize your potential and chance of victory, probably more so then a standard RPG will

Your style of play isn't unusual at all. Basically, you get a kick out of building. Whether it's building up a city and it's research, or building up an army with specialized units and equipment, or building up a character through skill trees and outfitting, the idea idea is to strengthen and improve your alter ego with the resources available. Most of the time, it takes both planning and attention to detail. In the end, there is the satisfaction of having reached "true power," and the joy of exercising that power by stomping your opponents into a grease spot.

The "growth" aspect of gaming has been around since Dungeons & Dragons and is an important part of most RPG's. The two extremes are "grinding" (e.g. Aion) and "parity" (e.g. Morrowind). Different people prefer different levels of effort required for growth. You want to pay attention to both how quickly you want the growth to occur, and to what extent you want your "final form" to be overpowered. Once you have that figured out, it's not difficult to identify games which will scratch that itch.

For myself, the epitome of my building style is "easy expansion, deep specialization." I like my character levels to come regularly, with only moderate grinding, and I like my skill trees to offer multiple paths to victory/power. Diablo II Lord of Destruction is one of my favorite games for that reason. My knowledge of the game allows me to level up quickly, and each of the six characters offers multiple ways to stomp the enemy. I just have to plan my path to power and build up my character. When I finally reach max level, I am able to blow away my enemies using whatever method I've chosen.

From the responses you've given in this thread, I would guess you to prefer "galaxy-conquering civilization" over "heroic titan of doom." You've already been given lots of RTS games that fit that build. One that hasn't been mentioned, yet, is the Age of Wonders franchise. That series combines both city/civilization building and hero-building, albeit in a fantasy setting. If you want less magic and more technology, Warlords Battlecry, Age of Empires II, and Ashes of the Singularity have already been mentioned.

Have you played Total War games where you auto-resolve every battle?
particularly the older games

If you haven't already, you probably want to check this out. It would seem to be right up your alley.