1 Tile broken in Lounge, Any way to fix without changing whole

Renovations
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Hi, I am recently shifted to new location and rented it, on 4th day, I saw this damage of the floor on lounge, I knew it is old issue, but it is fully broken now, so the owner will surely blame me for this, do you have any DIY or anything to fix it?

I have a little knowledge but I learnt that there is Dye lot thing, which means color be slightly difference, is it true?

I mean even If I order this white, is it possible that can be differ in real?

Not currently in a state to afford whole remodel.

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1935×1448 416 KB

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SimpleGrout #115 Platinum 1 qt. Pre-Mixed Grout https://www.homedepot.com/pep/Custom-Building-Products-SimpleGrout-115-Platinum-1-qt-Pre-Mixed-Grout-PMG115QT/319228473?g_store=&source=shoppingads&locale=en-US&fp=ggl&pla&mtc=SHOPPING-CM-CML-GGL-D23F-023_014_FLOOR_TOOLS-NA-NA-NA-PMAX-7066701-NA-NA-NA-NA-NBR-NA-NA-NEW-_FY26&cm_mmc=SHOPPING-CM-CML-GGL-D23F-023_014_FLOOR_TOOLS-NA-NA-NA-PMAX-7066701-NA-NA-NA-NA-NBR-NA-NA-NEW-_FY26-23716027611--&gclsrc=aw.ds&gad_source=1&gad_campaignid=23721337160&gclid=CjwKCAjwntHPBhAaEiwA_Xp6Rr_WJ-hLXAJZT2Z2x077OSMTcHtfkchV2Y6axduJr2rJ0vngv0PctRoCRQIQAvD_Bw

You will need this to reset new tile, yes dye lots are different, take broken piece to store with old tiles and try to match as close as possible, the trick is trying to remove one broken piece without disturbing the others around it, you will need a chisel and a hammer, along the edges, good luck