cmake does not find the includes

I'm incorporating the OpenTelemetry C++ library (v1.8.3) into my project using a CMake helper that creates "imported static" targets with their own include paths and .a files. However, when I link the opentelemetry-cpp::metrics target into a metrics submodule of my engine, the compiler can't find the OpenTelemetry SDK headers.

Makefile rule

### opentelemetry ###
${OPENTELEMETRY_LIB}:
	cd $(EXTERNAL_OPENTELEMETRY) && mkdir -p build && cd build && cmake .. -DCMAKE_BUILD_TYPE=Release -DBUILD_TESTING=OFF -DWITH_EXAMPLES=OFF -DOPENTELEMETRY_INSTALL=ON -DWITH_ABSEIL=OFF -DWITH_STL=ON -DWITH_BENCHMARK=OFF && ${MAKE}

/ruta/al/proyecto/
├── external/
│   └── opentelemetry-cpp-1_8_3/
│       ├── opentelemetry-cpp-1.8.3/
│       │   ├── api/
│       │   │   └── include/opentelemetry/…
│       │   └── sdk/
│       │       └── include/opentelemetry/sdk/metrics/…
│       └── build/
│           └── sdk/src/metrics/libopentelemetry_metrics.a
├── engine/                                    # target de nivel superior
│   ├── CMakeLists.txt                         # Here I define the helper
│   └── metrics/                               # submodule “metrics”
│       └── CMakeLists.txt                     # Here I link against OpenTelemetry
├── Makefile

Helper

function(add_manual_imported alias header_dir static_lib)
  string(REPLACE "::" "_" internal "${alias}")
  if(static_lib)
    add_library(${internal} STATIC IMPORTED GLOBAL)
    set_target_properties(${internal} PROPERTIES
      IMPORTED_LOCATION           "${static_lib}"
      INTERFACE_INCLUDE_DIRECTORIES "${header_dir}"
    )
  else()
    add_library(${internal} INTERFACE IMPORTED GLOBAL)
    set_target_properties(${internal} PROPERTIES
      INTERFACE_INCLUDE_DIRECTORIES "${header_dir}"
    )
  endif()
  add_library(${alias} ALIAS ${internal})
endfunction()

add_manual_imported(
  opentelemetry-cpp::metrics
  "${PROJECT_SOURCE_DIR}/../external/opentelemetry-cpp-1_8_3/opentelemetry-cpp-1.8.3/sdk/include"
  "${PROJECT_SOURCE_DIR}/../external/opentelemetry-cpp-1_8_3/opentelemetry-cpp-1.8.3/build/sdk/src/metrics/libopentelemetry_metrics.a"
)

so I link in the submodule engine/metrics/CMakeLists.txt

target_link_libraries(metrics
  PUBLIC
    metrics::imetrics
    base
  PRIVATE
    opentelemetry-cpp::metrics    # Here I use the imported target
)

Observed behavior

When compiling the metrics submodule, any line like

#include <opentelemetry/sdk/metrics/push_metric_exporter.h>

produces a “file not found” error

Additional Information

CMake Version: 3.24

Platform: Ubuntu 22.04

Start with engine/CMakeLists.txt and engine/metrics/CMakeLists.txt, focusing on add_manual_imported and the opentelemetry-cpp::metrics link. Reproduce the missing-header error on Ubuntu 22.04 with CMake 3.24 and inspect the imported target's include paths. Done means the metrics submodule can compile the stated OpenTelemetry SDK include.