Very strange waveform Shape

Hello,
I have reduced your example to a minimum to investigate in details.
I changed output to Serial and observe the signals via SerialPlot SW.
Input signal was Sine 1kHz, 2V Amp, 1.7V offset.

#include "ADCSampler.h"

#define SAMPLE_RATE 32000 //16000
#define SAMPLES 16384

#define TPIN 2
#define t1 digitalWrite(TPIN, HIGH);
#define t0 digitalWrite(TPIN, LOW);
#define t digitalWrite(TPIN, !digitalRead(TPIN));

ADCSampler *adcSampler = NULL;
I2SSampler *i2sSampler = NULL;

// i2s config for using the internal ADC
i2s_config_t adcI2SConfig = {
.mode = (i2s_mode_t)(I2S_MODE_MASTER | I2S_MODE_RX | I2S_MODE_ADC_BUILT_IN),
.sample_rate = SAMPLE_RATE, //16000,
.bits_per_sample = I2S_BITS_PER_SAMPLE_16BIT, // I2S_BITS_PER_SAMPLE_16BIT,
.channel_format = I2S_CHANNEL_FMT_ONLY_LEFT,
.communication_format = I2S_COMM_FORMAT_I2S_LSB,
.intr_alloc_flags = ESP_INTR_FLAG_LEVEL1,
.dma_buf_count = 4,
.dma_buf_len = 1024,
.use_apll = false,
.tx_desc_auto_clear = false,
.fixed_mclk = 0
};

void adcWriterTask(void *param)
{
I2SSampler *sampler = (I2SSampler *)param;
const TickType_t xMaxBlockTime = pdMS_TO_TICKS(100);
while (true)
{
uint32_t ulNotificationValue = ulTaskNotifyTake(pdTRUE, xMaxBlockTime);
if (ulNotificationValue > 0){
int8_t *buffptr = (int8_t*)sampler->getCapturedAudioBuffer();

// for (int i = 0; i < sampler->getBufferSizeInBytes(); i=i+2) {
// Serial.printf("%d\n\r", buffptr[i] + buffptr[i+1]*256);
// }
Serial.write((char *) sampler->getCapturedAudioBuffer(), sampler->getBufferSizeInBytes());
}
}
}

void setup()
{
Serial.begin(115200);
pinMode(TPIN, OUTPUT);
while (!Serial);

adcSampler = new ADCSampler(ADC_UNIT_1, ADC1_CHANNEL_7);

TaskHandle_t adcWriterTaskHandle;
xTaskCreatePinnedToCore(adcWriterTask, "ADC Writer Task", 4096, adcSampler, 1, &adcWriterTaskHandle, 1);
adcSampler->start(I2S_NUM_0, adcI2SConfig, SAMPLES, adcWriterTaskHandle);
}

void loop()
{
}

Below are screenshorts of the various I2S settings.
Please, note how awful they looks. They should be smooth but they did not.
Only at 32Bit 100kHz it looks acceptable.
First time I met the problem on PDM example for M5 Core2.
Note, also, that signals aquired from analogRead function are ideal.
This sawtooth distortion leave no way to use FFT because they produce a lot of harmonics. Also, the same thing occured in you original code(Audacity picture).
)

Start with the supplied ADCSampler.h-based example and the adcI2SConfig settings, then reproduce the 1 kHz input through Serial and SerialPlot at the listed sample rates and bit depths. Compare the captured waveform with analogRead and determine what causes the sawtooth distortion; done means the I2S capture is smooth enough for the reported FFT use case.

Written by the indexing model from the issue text.