Storing the last state of a relay in EEPROM of NodeMcu?

So in your original sketch you chose to connect your relay to D0, which is GPIO 16.
That’s not a good choice of pin, as it’s one of those ‘special’ pins. See this post:

NdeMCU EEPROM has a limited life - the manufacturers say that each memory location should be good for around 100,000 write operations.
Your original code writes to EEPROM every 100 milliseconds (or 10 times per seconds) so after less than three hours of running this code you will have exceeded the probable life of the memory location you’re using.
As @Lichtsignaal says, the data is stored o the Blynk server anyway, so use of EEPROM in this situation gains you nothing.

I also find this a bit odd…

So, on startup you’re reading the value from EEPROM and writing the value to the relay pin, then 10 milliseconds later overriding it by forcing it LOW. Why?

When people give you pointers to possible solutions, it’s time to take those suggestions and do a bit of experimenting, rather than asking “will this work”.

Pete.