Espidf-arduino-blink example fails for ESP32S2 but not for other Chips

So I would like to compile with
platform = espressif32, framework = arduino, espidf
for the board adafruit_qtpy_esp32s2.
and I started with the often cited Espidf-arduino-blink.

Fact: Just running the example as it is on github works well for the given predefined boards (esp32dev, espea32, esp320).
But when I add the following board lines (testing various boards, I always get the same errors for the esp32s2, see below).

platform = espressif32
framework = arduino, espidf
build_flags = 
monitor_speed = 115200

; [env:esp32dev]
; board = esp32dev

; [env:espea32]
; board = espea32

; [env:esp320]
; board = esp320

board = adafruit_qtpy_esp32s2

board = seeed_xiao_esp32c3

board = adafruit_qtpy_esp32

board = adafruit_feather_esp32s2_tft

Result of pio run:

Environment                   Status    Duration
----------------------------  --------  ------------
adafruit_qtpy_esp32s2         FAILED    00:00:38.389
seeed_xiao_esp32c3            SUCCESS   00:03:46.079
adafruit_qtpy_esp32           SUCCESS   00:03:59.153
adafruit_feather_esp32s2_tft  FAILED    00:00:44.090

The error I get is:

src/Blink.cpp: In function 'void setup()':
src/Blink.cpp:64:5: error: 'Serial' was not declared in this scope
src/Blink.cpp:64:5: note: suggested alternative: 'Serial1'
src/Blink.cpp: In function 'void loop()':
src/Blink.cpp:70:5: error: 'Serial' was not declared in this scope
src/Blink.cpp:70:5: note: suggested alternative: 'Serial1'

My trials of using Serial1 (reluctantly) did not work out. Also Serial0 did not work out. It seams, the framework compiles main() instead of setup and loop.

I found no esp32s2 board which I could compile the example with. All esp32s2 end up in the same error message. All the other boards I tried compile without any error.

Any idea how to fix this is highly appreciated. best regards