The ESP32S3 has a builtin uart interface that can be used as programmer and also as debugger. It means that is not necessary to use an external programmer, it works by itself. The way it works is the same.

The connections are the next:

or even directly to the chip like (USB-D- and USB-D+):

Install drivers

I had some problems to install it, but finally I got it working. I followed the next source

Basically is:

sudo apt-get install make libtool pkg-config autoconf automake texinfo libusb-1.0
cd /etc/udev/rules.d
wget https://raw.githubusercontent.com/espressif/openocd-esp32/master/contrib/60-openocd.rules 60-openocd.rules
cd
cd esp-idf-v5.0.1/openocd-esp32
./bootstrap
./configure
make
sudo make install

To test that is working launch the next:

openocd -f board/esp32c3-builtin.cfg

Debug in plarform io

When the previous is working you can create a project file like:

[env:esp32-s3-devkitc-1]
platform = espressif32
board = esp32-s3-devkitc-1
framework = arduino
debug_tool=esp-builtin

And then if you press debug it should works.