You need to compile the espruino firmware locally on your own PC. I did my compilation on:

$ uname -a
Linux kaki5 5.13.0-30-generic #33~20.04.1-Ubuntu SMP Mon Feb 7 14:25:10 UTC 2022 x86_64 x86_64 x86_64 GNU/Linux

One this we need to change in user_main.c under Espruino/targets/esp8266
$ diff user_main.c user_main.c-ORIG
353,382d352
< void ICACHE_FLASH_ATTR user_pre_init(void)
< {
< bool rc = false;
< static const partition_item_t part_table[] =
< {
< {SYSTEM_PARTITION_RF_CAL,
< 0x3fb000,
< 0x1000},
< {SYSTEM_PARTITION_PHY_DATA,
< 0x3fc000,
< 0x1000},
< {SYSTEM_PARTITION_SYSTEM_PARAMETER,
< 0x3fd000,
< 0x3000},
< };
<
< // This isn't an ideal approach but there's not much point moving on unless
< // or until this has succeeded cos otherwise the SDK will just barf and
< // refuse to call user_init()
< while (!rc)
< {
< rc = system_partition_table_regist(part_table,
< sizeof(part_table)/sizeof(part_table[0]),
< 4);
< }
<
< return;
< }
<
<
388d357
< user_pre_init();

The firmware would not compile without the user_pre_init(). Insert this block of code

void ICACHE_FLASH_ATTR user_pre_init(void)
{
bool rc = false;
static const partition_item_t part_table[] =
{

{SYSTEM_PARTITION_RF_CAL,
 0x3fb000,
 0x1000},
{SYSTEM_PARTITION_PHY_DATA,
 0x3fc000,
 0x1000},
{SYSTEM_PARTITION_SYSTEM_PARAMETER,
 0x3fd000,
 0x3000},

};

// This isn't an ideal approach but there's not much point moving on unless
// or until this has succeeded cos otherwise the SDK will just barf and
// refuse to call user_init()
while (!rc)
{

rc = system_partition_table_regist(part_table,
                                   sizeof(part_table)/sizeof(part_table[0]),
                                   4);

}

return;
}

Above the void user_init() function. Insert user_pre_init() as the first statement in the user_init() function

void user_init() {

  user_pre_init();
  system_timer_reinit(); // use microsecond os_timer_*
  ....

I do not use the Espruino/scripts/provision.sh to build, but my own simple script:

#!/usr/bin/sh
echo "----------------------------------------------------------"
echo "Building Espruino for ESP8266 4MB Flash"
export ESP8266_SDK_ROOT=/home/sharil/MJ/ESP8266_NONOS_SDK
export PATH=/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:pwd/xtensa-lx106-elf/bin/
echo GCC is $(which xtensa-lx106-elf-gcc)
rm espruinoesp8266
make clean

make V=1 RELEASE=1 BOARD=ESP8266_4MB

make V=1 RELEASE=1 BOARD=ESP8266_ME
echo "ESP8266 (4MB Flash) build done"
echo "----------------------------------------------------------"

Note that used ESP8266_ME board which is a copy of ESP8266_4MB.py with 'FILESYSTEM', 'FLASHFS' included in the libraries.

Please give it a try.