Thank you for your efforts in investigating.
While the cause remains unknown, I’ll continue to explore the issue further.

const uart_config_t uart_config = {
.baud_rate = 115200,
.data_bits = UART_DATA_8_BITS,
.parity = UART_PARITY_DISABLE,
.stop_bits = UART_STOP_BITS_1,
.flow_ctrl = UART_HW_FLOWCTRL_DISABLE,
.source_clk = UART_SCLK_DEFAULT,
};
// We won't use a buffer for sending data.
uart_driver_install ...

causes a 50-200ms pause on the UART TX in the middle of the transmission?

Yes,the following processing is implemented, causing a pause of 50 to 200 milliseconds during transfer.
The task running this process has the highest priority.

This issue involves sending 200 bytes of data, for example.
After transmitting the first 128 bytes, an interval of 50 to 200 milliseconds occurs,
followed by the transmission of the remaining 72 bytes.

This behavior has been confirmed using an oscilloscope.

We would like to understand why this ...

The baud rate is 115200. Since the TX buffer size specified in uart_driver_install() is 0, I assume the FIFO buffer is using the default size of 128 bytes.

I'm using ESP32-S3 and encountering occasional delays when sending more than 128 bytes (e.g., 200 bytes) via uart_write_bytes().
Normally, the notification completes within about 10ms, but sometimes it takes between 50ms and 200ms.
Even after setting the task priority to the maximum (24), the issue ...