Is it possible to use extra AVR Flash memory as non-volatile EEPROM-like Flash memory storage?
Yes you can. This Arduino IDE add on lets you make calls to code store in the bootload of memory so you can make changes to the flash memory.
https://majek.sh/en/writing-to-internal-flash-on-arduino/

The number of times you rewrite a cell are limited.
I'd suggest you are better off with adding a FRAM memory chip.
Get a 5V part with SPI interface. Fast reads, virtually unlimitless writes (trillions)
https://www.digikey.com/products/en/integrated-circuits-ics/memory/774?k=fram+memory&amp;k=&amp;pkeyword=fram+memory&amp;pv276=15&amp;FV=ffe00306%2C1f140000%2C1fec000b&amp;quantity=0&amp;ColumnSort=0&amp;page=1&amp;stock=1&amp;pageSize=25