I preface this reply by saying that it may step on some toes and is not for the easily offended... Think of your floor cleaning like your teeth cleaning: you can brush, floss, and gargle on your own to your heart's delight. But at the end of the day, it can't replicate the cleaning performed by a hygienist in the dentist office. In other words, you need to have a professional cleaning company periodically clean your vinyl floors. I know, most of you DYIers had it installed to get away from carpet, tile, and other flooring that has traditionally required professionals to maintain. Truth is, you DO NOT own the equipment needed to get these floors, particularly the ones with a textured profile, completely clean like they were prior to install. And while the flooring companies didn't outright lie to you (calling it low maintenance rather than no maintenance), they certainly led you astray by letting you to believe that a little hot water or their overpriced, product-specific cleaner was all you needed. So, find a reputable local cleaner to professionally clean your LVP floors. Got kids and dogs? Do you go barefoot or wear outdoor shoes in the house? Get your floors professionally cleaned every single year. The rest of you? Every 2-3 years. In the meantime, stop using steam. Stop using acidic (vinegar) and high ph (ammonia) products. Dump the bleach, Murphy's Oil Soap, Rejuvenate, Bona, Mop n Glow, Orange Glo, and all types of polishes. Only use a neutral cleaner in between professional cleanings. Oh, and those area rugs you put down to cover up the unsightliness of your floors? They're likely voiding your flooring warranty (probably not a big deal because many have already done so with their unapproved cleaning methods and lifestyle).

The floor likely has a 'wear layer' of UV cured very hard aluminum oxide clear from 12 to 20+mil thick. You will need to sand the finish to get the next coat to adhere. That coat(s) would be a primer. And then multiple coats of a topcoat. I'd guess at a roller applied boat paint. It's meant for this type of application. Kinda self-leveling. You must use products by the same manufacturer. And follow the recommended procedures. Perfection Pro topside paint by Interlux. A lot of work and the products are expensive. . . .It will not be as durable as the original finish because it will not be as thick. . . .So you may want to pull up the flooring and replace it with a rigid vinyl plank that you like the look of.

The picture you posted is a good floor. It’s rugged, waterproof and has a flat finish that shouldn’t show scratches. I used it in my home and love it.

It is very popular flooring category for sure. The price is from $3 to 7/sqft depending on the brand and thickness. Installation is from $2 to 4/sqft. on top of the material costs. LVP can be installed on the stairs. See below picture of Elegance Plyquet Luxe installed.