How can I specify the path to Ninja in VS Code CMake configuration without modifying my system's PATH environment variable?

As you can see I've tried a few approaches and none work:

CMakeSettings.json

{
    "configurations": [
        {
            "name": "riscv32",
            "generator": "Ninja"
        }
    ]
}

cmake-kits.json

[
  {
    "name": "riscv32-esp-elf-gcc",
    "isTrusted": true,
    "compilers": {
      "C": "/ProgramData/esp-idf-tools/tools/riscv32-esp-elf/esp-2022r1-11.2.0/riscv32-esp-elf/bin/riscv32-esp-elf-gcc.exe",
      "CXX": "/ProgramData/esp-idf-tools/tools/riscv32-esp-elf/esp-2022r1-11.2.0/riscv32-esp-elf/bin/riscv32-esp-elf-g++.exe"
    },
    "toolchainFile": "/ProgramData/esp-idf/tools/cmake/toolchain-esp32c3.cmake",
    "preferredGenerator": {
      "name": "Ninja"
    }
  }
]

settings.json

{

    "cmake.cmakePath": "/ProgramData/esp-idf-tools/tools/cmake/3.24.0/bin/cmake.exe",
    "cmake.configureArgs": [
        "-DCMAKE_MAKE_PROGRAM=/ProgramData/esp-idf-tools/tools/ninja/1.10.2/ninja.exe"
    ],
    "cmake.buildArgs": [
        "-DCMAKE_MAKE_PROGRAM=/ProgramData/esp-idf-tools/tools/ninja/1.10.2/ninja.exe"
    ],
    "cmake.additionalCompilerSearchDirs": [
        "/ProgramData/esp-idf-tools/tools/ninja/1.10.2"
    ]
}

On load I always get

[proc] The command: ninja --version failed with error: Error: spawn ninja ENOENT
[proc] The command: ninja-build --version failed with error: Error: spawn ninja-build ENOENT
[main] Unable to determine what CMake generator to use. Please install or configure a preferred generator, or update settings.json, your Kit configuration or PATH variable. Error: No usable generator found.

I want to avoid adding (yet another) entry to the operating system's PATH.

This was deeply frustrating, but I did eventually stumble into a solution.

Nothing in settings.json helps. The only setting that takes any effect is in cmake-kits.json:

[
  {
    "name": "riscv32-esp-elf-gcc",
    "isTrusted": true,
    "compilers": {
      "C": "/ProgramData/esp-idf-tools/tools/riscv32-esp-elf/esp-2022r1-11.2.0/riscv32-esp-elf/bin/riscv32-esp-elf-gcc.exe",
      "CXX": "/ProgramData/esp-idf-tools/tools/riscv32-esp-elf/esp-2022r1-11.2.0/riscv32-esp-elf/bin/riscv32-esp-elf-g++.exe"
    },
    "toolchainFile": "/ProgramData/esp-idf/tools/cmake/toolchain-esp32c3.cmake",
    "preferredGenerator": {
      "name": "Ninja"
    },
    "environmentVariables": {
      "PATH": "/ProgramData/esp-idf-tools/tools/ninja/1.10.2;${env:PATH}"
    }
  }
]