Patch for Tile Sealant Coat

I have a problem with the tiles around the tub in my ~1910 residential apartment building in Washington DC.

At some point the existing tile was coated in some sort of sealant layer, which has developed a hole (approx. 3" x 3") as shown in the picture. Ideally I would like to patch the hole somehow, but I am open to any suggestions about the best way to proceed.

Here is some additional information:

• The tile underneath the hole is cracked. However, I have been told that the tiles are set in concrete and extremely difficult to remove. I am open to solutions that involve removing and replacing the old tile, or leaving it in place beneath a patch.
• The hole is currently covered in packing tape, which can also be seen in the picture.
• Color match is a secondary concern to water-tightness.
• We intend to remove and replace the caulk around the tub at the same time.

Please let me know if you have any other questions that might help.

Source: https://diy.stackexchange.com/questions/155548/patch-for-tile-sealant-coat