It looks like the grout is low enough that you could get away with a thorough cleaning and re grout the space. I would probably get a vibrating multi tool and grout blade to rough up all the grout first.

Steam cleaning works pretty well if you don't want to do all that work.

The best and most expensive option is re tile. I have never taken on a grout refinishing job as a professional.

Shipping costs are a huge part of retail prices.

DAP is great. Alex plus is good as well; that's what I use when I professionally remodel bathrooms and kitchens.

They make commercial cleaning tablets that work well. I also have used an Ozone generator but they are pretty dangerous.