From the looks of it, you did not point CMake to your custom Qt installation. Check CMAKE_PREFIX_PATH.

sudo apt install qtbase5-private-dev qt6-tools-dev qt6-l10n-tools

error changed to

CMake Error at /usr/lib/x86_64-linux-gnu/cmake/Qt6Network/Qt6NetworkPlugins.cmake:5 (__qt_internal_include_plugin_packages):
  Unknown CMake command "__qt_internal_include_plugin_packages".
Call Stack (most recent call first):
  /usr/lib/x86_64-linux-gnu/cmake/Qt6Network/Qt6NetworkConfig.cmake:131 (include)
  /usr/lib/x86_64-linux-gnu/cmake/Qt6/Qt6Config.cmake:219 (find_package)
  CMakeLists.txt:49 (find_package)

find_package(ECM 5.240.0 REQUIRED NO_MODULE)

I changed it to

find_package(ECM REQUIRED NO_MODULE)

Next I install from sources Qt 6.5.2 with standard prefix /usr
and changed

set(REQUIRED_QT_VERSION 6.4.0)
find_package(Qt6 ${REQUIRED_QT_VERSION} NO_MODULE REQUIRED COMPONENTS Core Network Test)

to

find_package(Qt6 NO_MODULE REQUIRED COMPONENTS Core Network Test)

now is not QT_INSTALL_PREFIX, still error with CorePrivate

-- Performing Test HAVE_STDATOMIC - Success
-- Found WrapAtomic: TRUE  
CMake Error at /usr/lib/cmake/Qt6Core/Qt6CoreVersionlessTargets.cmake:37 (message):
  Some (but not all) targets in this export set were already defined.

  Targets Defined: Qt::Core

  Targets not yet defined: Qt::CorePrivate

Call Stack (most recent call first):
  /usr/lib/cmake/Qt6Core/Qt6CoreConfig.cmake:55 (include)
  /usr/lib/cmake/Qt6/Qt6Config.cmake:157 (find_package)
  CMakeLists.txt:46 (find_package)


-- Configuring incomplete, errors occurred!
See also "/home/andrzej/wazne/gitmy/syntax-highlighting/build/CMakeFiles/CMakeOutput.log".

note: if I change Qt6 to Qt5 is without cmake errors, but unfortunately in .cpp code is used QList.data() which is error in Qt5

How did you point cmake to your custom Qt build ?