How Many EEPROM Write Cycles Left in My EEPROM

No, there is no way to know how many times they have been programmed. A typical user will only program them a few times, so you should be OK. If you plan on programming them tens of thousands of times, you should get new parts.

EEPROMs from the factory are normally unprogrammed (all 1's).

100,000 writes is a "guarantee", they won't magically die at this number. A typical part will last much longer.

As others have indicated a typical EEPROM at room temperature can do many, many more than the guaranteed 100'000 write.

There have been many tests of these performed such as:

Hackaday EEPROM killer