I was a complete fool, yes the code is not identical and it does work as intended.

static inline void ulp_riscv_gpio_output_level(gpio_num_t gpio_num, uint8_t level)
{
if (level) {
REG_SET_FIELD(RTC_GPIO_OUT_W1TS_REG, RTC_GPIO_OUT_DATA_W1TS, BIT(gpio_num));
} else {
REG_SET_FIELD(RTC_GPIO_OUT_W1TC_REG, RTC_GPIO_OUT_DATA_W1TS, BIT(gpio_num));
}
}


Code for if(level) and ...

Finally I got it working and I blame poor documentation for my problem. Looking how the RiskV ULP initializes the rtc i2c I found this:
/* For esp32s3, we need to enable the rtc_i2c clock gate before accessing rtc i2c registers */
SET_PERI_REG_MASK(SENS_SAR_PERI_CLK_GATE_CONF_REG, SENS_RTC_I2C_CLK ...

Use neither as both are bloated. I use geany which works nicely.
If you want I post the Geany configuration I use.

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "freertos/FreeRTOS.h"
#include "freertos/task.h"

#define TAG "test_write_rtc_reg.c"

#if ESP_IDF_VERSION_MAJOR < 5
#include "driver/rtc_cntl.h"
#else
#include "esp_private/rtc_ctrl.h"
#endif

#include "driver/rtc_io.h"
#include ...

Thank you for answering that quickly. What you said makes a lot of sense, however I can
use the RTC GPIO without any problems. How can I turn the RTC power domain on or off to
double check?

I want to initialize the RTC I2C controller using the main processor of the ESP32-S3
As en example setting RTC_I2C_SCL_LOW_REG

SET_PERI_REG_BITS(RTC_I2C_SCL_LOW_REG, RTC_I2C_SCL_LOW_PERIOD_REG, 40, RTC_I2C_SCL_LOW_PERIOD_REG_S); // SCL low/high period = 40, which result driving SCL with 100kHz ...

i was able to fix that myself.
The working code is here:
https://github.com/cbaurtx/ESP32_keypad_rotdecode

I did some digging...
It seems that the command ulp_embed_binary creates executables only. So no code for libraries

That was the wrong example (ULP and not a custom component)
So here you go....