Maybe I'm obtuse but why not just get a longer rug so the cracked tiles are covered?

I installed marble counters and there was a crack that had to be repaired. The crack is now completely unnoticeable and I have been told that the process creates a strong bond. If I had been dissatisfied with the result, I would have had them reinstall with a new counter and I am glad that it became a non-issue in terms of both aesthetics as well as durability/functionality.

Have the tile professionally cleaned to remove the ground-in dirt in cracks. Bring home some paint chips and match the cleaned-up tile color. Buy a quart of semi-gloss or high gloss enamel. Then find an unobtrusive place to practice applying it. In some cases, you can mix a couple bottles of white and beige "porcelain appliance repair paint" from your local hardware or big box store so that it matches. It is fussy but easy work to do a pretty good job with a tiny brush.

A good tile guy can repair these cracks so they will not get larger or get filled with dirt.

More will probably break--they probably aren't installed quite solidly enough. You can definitely make these look better with cleaning and filling, but it'll probably end up like the time I dropped my favorite Pyrex bowl on my tile floor...and broke the floor.

TL;DR: you're gonna need a bigger rug. https://esalerugs.com/11-ft-runner-rugs

Do the closets have same tile? Remove them & replace broken ones in view.

For heavens sake. How do you even open the DW??? 2' x 9' 10" below

https://esalerugs.com/dark-gray-10-ft-runner-monaco-area-rug-33141472

No problems opening DW or oven. You just have to stand to the side. Not used to NYC apartment, huh ;) ?

I like the one you posted above.

@gargigg - I'm also in a high rise and thought that remark by Jan Moyer was out of left field.

The dishwasher door goes down and you load to the side. If anyone is frantic to access something that is blocked by the door, it goes up temporarily. Same with refrigerator doors that are open and temporarily block the aisle.

The out of left field was whoa that is REALLY a tight galley. : )

I think the main concern is why are cracks forming. Is it due to poor quality tiles, poor installation, or the worst case scenario, the floor/building is settling and causing the tiles to crack.

It's not just NYC. My first house in Toronto had a galley kitchen that was just as narrow and short.

So many pros vying to take Sophie's place!

If you just decide to use a larger runner until you can replace the floor, have you considered a remnant? I have seen some beautiful geometric patterned carpet, and larger retailers have extensive displays of remnants reasonably priced. All carpet comes in 12 foot lengths, and if you only need a 2 foot width, they might even give it to you for the cost of binding. In PA binding is $2 per linear foot. Good luck!