Hello drowsell,
If you would like to save some data to flash, you could use AT+SYSMFG command to make it: https://docs.espressif.com/projects/esp-at/en/latest/esp32c3/AT_Command_Set/Basic_AT_Commands.html#cmd-sysmfg

For example, you want to save "hello world", you can send AT+SYSMFG=2,"factory ...

Today I continued to work on this. I used the ESP-IDF to change my partition to look like the following:

partitions.csv
[Codebox]# Name, Type, SubType, Offset, Size
phy_init, data, phy, 0xd000, 0x1000
nvs, data, nvs, 0xe000, 0xE000
at_customize, 0x40, 0, 0x1E000, 0x262000
factory, app, factory ...

Hello I am flashing my ESP-C3-WROOM-02 with the following command:

[Codebox]python -m esptool -p COM7 -b 921600 --before default_reset --after hard_reset --chip esp32c3 write_flash --flash_mode dio --flash_size 4MB 0x8000 partition_table/partition-table.bin 0xd000 ota_data_initial.bin 0xf000 phy ...