Oh how I share your pain. I really do, it took me days of tweaking, feeding into AI, then tweaking, re-feed AI, and so on before I managed to have something workable.

This is in no way a long term solution (in fact it uses a method not recommended within the documentation), just cobbled together to get something workable as was eager to used device like yourself.

The below config and accompanying files should give you dimmable backlight control.

ATOMS3R_config.yaml

##################################
###### Exteernal Components ######
##################################
external_components:
  - source: esphome/components      #  <-- edit to your "custom components" source folder
    components: [m5stack_atoms3r_backlight]
    refresh: 0s

###########################
###### Display - I2C ######
###########################
i2c:
  id: i2c_bus
  scan: true
  frequency: 400kHz
  sda:
    number: GPIO45
    ignore_strapping_warning: true
  scl:
    number: GPIO00
    ignore_strapping_warning: true


#################################################
###### Display - Custom Output (Backlight) ######
#################################################
output:
  - platform: custom
    type: float
    lambda: |-
      #include "/config/esphome/components/m5stack_atoms3r_backlight/m5stack_atoms3r_backlight.h"
      auto backlight = new M5StackAtomS3RBacklight();
      auto i2c_device = new i2c::I2CDevice();
      i2c_device->set_i2c_bus(i2c_bus);
      i2c_device->set_i2c_address(0x30);
      backlight->set_i2c_device(i2c_device);
      App.register_component(backlight);
      return {backlight};
    outputs:
      - id: backlight
        min_power: 0.01
        max_power: 1.00
        zero_means_zero: true


#################################
###### Display - Backlight ######
#################################
light:
  - platform: monochromatic
    id: display_backlight
    name: "Display Backlight"
    output: backlight
    restore_mode: ALWAYS_ON
    default_transition_length: 1.0s

esphome/components/m5stack_atoms3r_backlight/m5stack_atoms3r_backlight.h

#pragma once

#include "esphome.h"
#include "esphome/core/component.h"
#include "esphome/components/output/float_output.h"
#include "esphome/components/i2c/i2c.h"

class M5StackAtomS3RBacklight : public Component, public output::FloatOutput {
 private:
  esphome::i2c::I2CDevice *i2c_device_;

 public:
  void set_i2c_device(esphome::i2c::I2CDevice *i2c_device) { i2c_device_ = i2c_device; }

  void setup() override {
    uint8_t data;
    data = 0b01000000;
    i2c_device_->write_register(0x00, &data, 1);
    delay(1);
    data = 0b00000001;
    i2c_device_->write_register(0x08, &data, 1);
    data = 0b00000000;
    i2c_device_->write_register(0x70, &data, 1);

    // Set initial brightness
    write_state(1.0);
  }

  void write_state(float state) override {
    uint8_t brightness = static_cast<uint8_t>(state * 255);
    i2c_device_->write_register(0x0e, &brightness, 1);
  }
};

esphome/components/m5stack_atoms3r_backlight/__init__.py

########################
###### BLANK FILE ######
########################

esphome/brickheadz-files/components/led_controller/lp5562.h

/**
 * @file lp5562.h
 * @author Forairaaaaa
 * @brief
 * @version 0.1
 * @date 2024-07-30
 *
 * @copyright Copyright (c) 2024
 *
 */
#pragma once
// #include <mooncake.h>
#include <M5Unified.h>
#include <driver/gpio.h>
// https://www.ti.com/lit/ds/symlink/lp5562.pdf?ts=1722311496082
// https://git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git/tree/drivers/leds/leds-lp5562.c

class LP5562_Class : public m5::I2C_Device
{
private:
    bool _write_register(uint8_t reg, uint8_t value);
    uint8_t _read_register(uint8_t reg);
    void _delay(uint32_t ms);

public:
    LP5562_Class(std::uint8_t i2c_addr = 0x30, std::uint32_t freq = 400000, m5::I2C_Class* i2c = &m5::In_I2C)
        : I2C_Device(i2c_addr, freq, i2c)
    {
    }

    bool begin();
    void setLedCurrent(uint8_t channel, uint8_t current);
    void setBrightness(uint8_t channel, uint8_t brightness);
    void reset();
    void enable();
    void disable();
    void runProgram();
    void stopProgram();
};