Concrete "tile look" floors are pretty popular now. In my previous home we had concrete in the living room (meant as a temporary measure after nasty carpet was removed, it lasted 3+ years). DH painted the floor with latex paint and covered with several coats of oil-based poly. Held up great. But we didn't have the pseudo-grout-line cracks you have. I don't know what your floors are sealed with, but we used vinegar and water to mop with. For regular cleaning though, we just used a vaccuum with a "bare floor" setting. I think that once the "grout-lines" are cleaned out, that you would be able to keep them clean just by vaccuuming regularly. Perhaps a grout brush would be helpful in cleaning out the cracks? Not sure what you mean by "spots, grease, scum" that won't come up with mopping - do you think that the concrete might have been been dirty before they sealed it? If so, they're there for good. If it's on top of the sealer, it should come off with 409 or some other general purpose cleanser.

I have concrete floors. I live in an area that can have snow from thanksgiving to end of Feb. I have radiant floor heat. It's amazing. I wanted the color you have posted on my floor but I have a huge wall of windows that face south west. I could only do water staining which can only go so dark instead of acid staining. I was told the acid stain over time will turn black where the sun hits. No thank you to unpredictable floors. Any scratches I get in the floor easily waxes out. It will break every dish or glass you drop without worrying about chipping or cracking or denting the floor. Invest in GelPro mats at kitchen work stations. I clean mine with one of those nubby microfiber dust mops. Sometimes I have to wipe up a spot with water and a rag.

So long as you realize the cost of properly stained and FINISHED concrete is more expensive than a 'laminate' or a mid-grade engineered hardwood then you are free to do what makes you happy. Most people think stained and finished concrete floors are an economical choice. It is not. It can be one of the most expensive floors we have. A beautifully stained (3 colour mix) and finished (clear epoxy) concrete floor STARTS around $12 - $15/sf and is a 'project' for a concrete flooring expert (usually more of an artist than a construction worker). Things to remember: Concrete is MORE DELICATE than marble. It is MORE POROUS than marble. It is easier to STAIN than marble (accidental stains as well as purposeful stains like purple and blue swirls). Concrete ETCHES (gloss changes = acid etching). Water can stain AND etch bare concrete floors. To prevent these nasty surprises you need to add a 'finish' to the floor. You can work with a low-level 'wax' or polish. These need +++ maintenance. You can add a urethane based finish. These last about 2 years and need ++maintenance. You can go up the ladder to epoxy = expensive but has ZERO maintenance. And then there is the reality of living with concrete. My flooring experience says most concrete floors are 'covered up' within 7 years. So you might want to keep all of this in mind. I would hate for you to create a work of art on your floors ($17/sf after everything is paid for) only to HATE living on it/with it and wanting to cover it up inside of 7 years. That's a lot of money to throw away on a floor you hate. If you need an understanding of how life is on concrete, go to Costco and stand/walk on their concrete floors for 8+ hours. Look down at the floors. Notice all the stains, all the etched spots. Notice all the CRACKS. Notice every flaw you can find. Stare at it. Decide if you can deal with this on a daily/hourly basis. Consider the floors at Costco are WELL maintained and they still look like that! Just a hint.

Basic Coating has a low VOC hybrid stain product line called Hypertone. It's been out a few years now. It can be difficult to get with limited suppliers. VOC is below 250. The lowest for oil base stains is 250 VOC (Absco and Poloplaz). Link is below: https://www.basiccoatings.com/solutions/hypertone-stains