Strip the python path for cmd.exe, name rules by kind, take the resolved install

The build.ninja python variable goes through strip_win_long_path_prefix
like every other emitted binary path (the NSIS launcher's extended
prefix cannot be spawned by cmd.exe). Compile rules are named by the
shared source kinds directly, retiring the identity translation table
and its drift test. write_project takes the caller's resolved ccache,
get_flash_ld_path reads the InstalledPaths the ninja file linked
against instead of re-resolving the version, the board backstop checks
the one table it indexes with an honest comment, and cc/cxx/ar paths go
through the shared toolchain_tool accessor (gaining the Windows
suffix).

tests/unit_tests/build_gen/test_arduino8266.py

@@ -69,13 +69,6 @@ def _shq(tok: str) -> str:
     return f'"{tok}"' if os.name == "nt" else f"'{tok}'"
 
 
-def test_rule_map_covers_all_source_suffixes() -> None:
-    """Every suffix a library manifest can select must map to a ninja rule."""
-    from esphome.platformio.library import SRC_FILE_EXTENSIONS
-
-    assert set(arduino8266._RULE_FOR_SUFFIX) == set(SRC_FILE_EXTENSIONS)
-
-
 def _resolve(*flags: str):
     """Set the build flags and resolve the knob config in one step."""
     _set_flags(*flags)
@@ -221,9 +214,8 @@ def _write_ninja(
             "esphome.arduino.library.resolve_libraries",
             return_value=libraries or [],
         ),
-        patch("esphome.arduino8266.framework.ccache_path", return_value=ccache),
     ):
-        arduino8266.write_project(paths)
+        arduino8266.write_project(paths, ccache)
     return (CORE.relative_pioenvs_path(CORE.name) / "build.ninja").read_text()
 
 
@@ -299,7 +291,7 @@ def test_write_project_link_line_and_exclusions(tmp_path: Path) -> None:
     assert "core_esp8266_main.cpp.o" in content
     # Assembly and C sources compile through their own rules
     assert "cont.S.o: asm" in content
-    assert "abi.c.o: cc" in content
+    assert "abi.c.o: c" in content
     # throw_stubs is force-included for ESPHome sources only, via one shared
     # srcflags variable rather than a copy of the flags line per edge
     src_lines = [line for line in content.splitlines() if "obj/src/" in line]
@@ -547,25 +539,21 @@ def test_write_project_libraries_and_variant(
 
 def test_get_flash_ld_path(tmp_path: Path) -> None:
 
+    paths = InstalledPaths(
+        framework=tmp_path / "framework",
+        toolchain=tmp_path / "toolchain",
+        ninja=Path("ninja"),
+    )
     CORE.testing_mode = True
-    assert get_flash_ld_path(tmp_path) == (
+    assert get_flash_ld_path(tmp_path, paths) == (
         tmp_path / "ld" / "testing_eagle.flash.4m.ld"
     )
 
     CORE.testing_mode = False
-    with (
-        patch(
-            "esphome.arduino8266.framework.get_framework_path",
-            return_value=tmp_path / "framework",
-        ),
-        patch(
-            "esphome.arduino8266.framework.framework_package_version",
-            return_value="3.30102.0",
-        ),
-    ):
-        assert get_flash_ld_path(tmp_path) == (
-            tmp_path / "framework" / "tools" / "sdk" / "ld" / "eagle.flash.4m.ld"
-        )
+    # Reads the same install the ninja file linked against; no re-resolve
+    assert get_flash_ld_path(tmp_path, paths) == (
+        tmp_path / "framework" / "tools" / "sdk" / "ld" / "eagle.flash.4m.ld"
+    )
 
 
 def test_flash_size_str() -> None:
@@ -756,8 +744,8 @@ def test_write_project_returns_changed(tmp_path: Path) -> None:
         patch("esphome.arduino.library.resolve_libraries", return_value=[]),
         patch("esphome.arduino8266.framework.ccache_path", return_value=None),
     ):
-        assert arduino8266.write_project(paths) is True
-        assert arduino8266.write_project(paths) is False
+        assert arduino8266.write_project(paths, None) is True
+        assert arduino8266.write_project(paths, None) is False
 
 
 def test_write_project_missing_elf2bin_raises(tmp_path: Path) -> None:
@@ -774,7 +762,7 @@ def test_write_project_missing_elf2bin_raises(tmp_path: Path) -> None:
         patch("esphome.arduino.library.resolve_libraries", return_value=[]),
         pytest.raises(EsphomeError, match="elf2bin"),
     ):
-        arduino8266.write_project(paths)
+        arduino8266.write_project(paths, None)
 
 
 def test_write_project_missing_src_dir_raises(tmp_path: Path) -> None:
@@ -789,7 +777,7 @@ def test_write_project_missing_src_dir_raises(tmp_path: Path) -> None:
         ),
         pytest.raises(EsphomeError, match="source directory"),
     ):
-        arduino8266.write_project(paths)
+        arduino8266.write_project(paths, None)
 
 
 def test_build_config_custom_mmu_without_knob_raises() -> None: