Clang-tidy breaks the code instead of fixing it

I just started using platformio but I am facing many problems with clang-tidy and some with cppcheck.

When I run pio check I get the following errors:

Checking esp32-s3-devkitc-1 > clangtidy (board: esp32-s3-devkitc-1; platform: espressif32; framework: arduino)
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src/App.h:6: [medium:warning] variable 'App' is non-const and globally accessible, consider making it const  [cppcoreguidelines-avoid-non-const-global-variables]
src/display/Display.cpp:4: [medium:warning] method 'create_display' can be made static  [readability-convert-member-functions-to-static]
src/display/Display.h:6: [medium:warning] variable 'Display' is non-const and globally accessible, consider making it const  [cppcoreguidelines-avoid-non-const-global-variables]
src/display/Display.h:6: [medium:warning] destructor of 'Display' is public and non-virtual  [cppcoreguidelines-virtual-class-destructor]
src/display/SerialDisplay.cpp:5: [medium:warning] method 'show_text' can be made static  [readability-convert-member-functions-to-static]
src/display/SerialDisplay.cpp:7: [medium:warning] variable 'buffer' is not initialized  [cppcoreguidelines-init-variables]
src/display/SerialDisplay.h:7: [medium:warning] variable 'SerialDisplay' is non-const and globally accessible, consider making it const  [cppcoreguidelines-avoid-non-const-global-variables]
src/display/SerialDisplay.h:7: [medium:warning] variable 'Display' is non-const and globally accessible, consider making it const  [cppcoreguidelines-avoid-non-const-global-variables]
src/main.cpp:7: [medium:warning] variable 'app' is non-const and globally accessible, consider making it const  [cppcoreguidelines-avoid-non-const-global-variables]
src/main.cpp:7: [medium:warning] variable 'app' provides global access to a non-const object; consider making the pointed-to data 'const'  [cppcoreguidelines-avoid-non-const-global-variables]
src/main.cpp:14: [medium:warning] assigning newly created 'gsl::owner<>' to non-owner 'App *'  [cppcoreguidelines-owning-memory]
================================================================================================================ [PASSED] Took 0.08 seconds ================================================================================================================
Checking esp32-s3-devkitc-1 > cppcheck (board: esp32-s3-devkitc-1; platform: espressif32; framework: arduino)
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src/App.cpp:10: [low:style] The function 'update_text' is never used. [unusedFunction]
src/display/Display.cpp:4: [low:style] The function 'create_display' is never used. [unusedFunction]
src/display/SerialDisplay.cpp:5: [low:style] The function 'show_text' is never used. [unusedFunction]

In particular, these two get auto-fixed breaking the code:

src/display/Display.cpp:4: [medium:warning] method 'create_display' can be made static  [readability-convert-member-functions-to-static]
src/display/SerialDisplay.cpp:7: [medium:warning] variable 'buffer' is not initialized  [cppcoreguidelines-init-variables]

these two do not make sense to me, because those are classes definition not variables

src/display/SerialDisplay.h:7: [medium:warning] variable 'SerialDisplay' is non-const and globally accessible, consider making it const  [cppcoreguidelines-avoid-non-const-global-variables]
src/display/SerialDisplay.h:7: [medium:warning] variable 'Display' is non-const and globally accessible, consider making it const  [cppcoreguidelines-avoid-non-const-global-variables]

all the cppcheck unusedFunction also do not make sense, given that those methods are indeed used

Can someone help me understanding what is going on and how to fix these problems?

I had no problem with clang-tidy in non-embedded C++ projects in the past.

Here there is an example code to reproduce the issues: