I checked the user_config.h file and ...
// The firmware supports a range of Flash sizes, though 4 Mbyte seems to be
// the most common currently. NodeMCU builds include a discovery function
// which is enabled by FLASH_AUTOSIZE, but you can override this by commenting
// this out and enabling the explicitly size, e.g. FLASH_4M. Valid sizes are
// FLASH_512K, FLASH_1M, FLASH_2M, FLASH_4M, FLASH_8M, FLASH_16M.
//#define FLASH_AUTOSIZE
#define FLASH_4M
assuming that something went wrong with https://nodemcu-build.com/ and/or FLASH_AUTOSIZE
I built the binary for the FLASH_1M, you will find them here
I tested the same binaries for the 4M flash and the client application and they are working fine
but I cannot test the 1M version because I'm missing such a devices
follow following steps:
1) erase the flash
2) flash 0x00000.bin at 0x00000
3) flash 0x10000.bin at 0x10000
4) reset the device
5) wait a few minutes for the file system formatting
6) reset it again
7) try to connect with ESPlorer
looks like the SDK 3 can generate the missing init data, so you can skip that step (it worked for me)