Painted grout will IMO never stand up to foot trafic and washing all the time . I have no idea of the aq footage you are dealing with but $700 seems to be a good deal for a whole main floor What color was the grout origianlly to me it looks fine so I need more info.

It would still have to be cleaned before it was painted. Is it actually stained, or just a dark grout. I have similar tile in my bathroom and the grout is the same color. (I don't love it either)

I agree, the companies that come in do a great job. When I had a lot more energy, I used to get down on my hands and knees and use a brush and Clorox cleanup to clean the grout once a year, that works great but it’s a pain and it smells awful. But I wouldn’t paint it, no way. Cute dog!

The original color of the grout was a light taupe. It was never sealed.

Before using bleach, consider that it may be damaging to grout.

IME, professional tile and grout cleaning are worth every nickel.

I bought a steamer with special brushes for cleaning grout. Works a charm but takes a long time. There are more heavy duty ones available too. This is the one we have

https://www.homedepot.com/p/DUPRAY-Neat-Steam-Cleaner-Multi-Purpose-Heavy-Duty-Steamer-for-Floors-Cars-Home-Use-and-More-DUP020WNA/312415048?source=shoppingads&locale=en-US

In my former home I had about 600sf of 4" tile with discolored sahara beige grout. It was recessed among a thousand squares of sharp edged unglazed quarry tile. MILES of grout! No surface cleaning machine will scrub the grout if it is recessed and the scrub pads will clean the tile and float there. I talked to equipment rental places regarding disc floor machines with pads and brushes and was told it really wouldn't make great contact down there. I manually tried many chemicals, stopping short of carcinogens. I used stuff that should not be used on grout including oven cleaner and the most effective was Lysol 10x toilet cleaner in the black bottle. I had an industrial strength steamer that cleaned but didn't remove discoloration. In the end, the toilet cleaner and a battery powered brush like this at Amazon was what worked the best. It was tedious and messy and I used dozens of rags to wipe up and rinse, doing this over a long period of time. It never looked like new and despite being "clean", it was not uniform in color. I was a tough critic, though, and it was probably fine for most people. Of course I sealed it afterward. If you choose to hire someone, ask if they will do a sample section so you can determine if it will clean to a uniform color. Instead of the painted on stuff that will not last (and looks like paint IMO), I wonder if there is a stain like product that would darken porous grout. Good luck with this.

Make a strong solution of Oxy Clean Powder and water. Wet floor good and keep wet for 30 minutes. Use a grout scrubbing brush on long handle to clean grout. Rinse well. When completely dry seal. Long handle grout brush can be found at cleaning supply stores.