Replacement for kitchen floor ideas?

Did you seal the grout? And no you can't add new flooring over tile. For one it is a tripping hazard from each area adjoining the kitchen. Furthermore it will never be stable and not to code. What I would do is have the tile professionally cleaned and sealed then see how you do. Or just change the flooring completely.

Naomie is right that trying to install another type of flooring over top of tiles will lead to many problems. One unsafe result is that it will raise the height of the floor up too high to match with the transition pieces in any doorways, closets, or adjoining other rooms.

You might be thinking of hardwood or laminate over tile, this would make you tile the base layer or subfloor. The tile would have to be perfectly level and all the grouting filled in. The lines of the grouting (if left unfilled) could collect moisture underneath the cracks and do serious damage to your newly installed floor.

How about a washable rug to cover most of it? Ruggable makes great ones.

If the only issue is the grout, you can paint it and then seal it. Make sure you re seal each year to avoid this issue again in the future.

If you want to put new flooring, like laminate, you will need to put down a thin barrier like luan plywood. If you don't you will have indentions in the new flooring where the grout lines are presently.

here is some info for you- they make tile that looks like wood but luxury vinyl is easy to clean and won't scratch, etc

https://www.bostonglobe.com/can-you-lay-new-floor-over-tile/AD05cFxyzdwcKGF8uyF9aI/story.html#:~:text=Yes%2C%20you%20can%20lay%20engineered,cause%20your%20install%20to%20fail.&text=You%20will%20need%20to%20use,floated%2C%20depending%20on%20the%20manufacturer.

you could use an electric floor scrubber to clean the tile and grout or use a cleaner you can buy at any hardware store or home depot, etc it takes a lot of elbow grease to clean the grout and then when it dries you can seal it and it is easier to clean

What about this? It shows how to install vinyl plank over old tile. https://www.youtube.com/watch?v=x88FOvM1sdI

Grout needs to be sealed. It's naturally porous and will stain easily.

Maybe stained concrete with a nice gloss sealer.