Mismatch between --no-color and NO_COLOR behavior in Sphinx 9.1.0 on Windows

Describe the bug

There appears to be a behavior mismatch between the command-line flag --no-color and the NO_COLOR environment variable:

1. --no-color still outputs ANSI control sequences (not colorized text, but cursor/line control sequences like \x1b[2K) on my Windows setup.
2. NO_COLOR=1 does not output these sequences.

Consequence: Users trying to disable terminal formatting get different behavior depending on which mechanism they choose.

Expected behavior: The behavior should be consistent, or clearly documented if intentionally different. (Personally, I think --no-color should produce fully ANSI-free output suitable for log files.)

How to Reproduce

This script sets up minimal docs and runs the test matrix. Just run it in a Python env that has Sphinx installed.

import os
from pathlib import Path
import subprocess
import sys
import tempfile


with tempfile.TemporaryDirectory() as tmp:
    src = Path(tmp) / "src"
    src.mkdir()
    (src / "conf.py").write_text("project = 'test'\n")
    (src / "index.rst").write_text("Test\n====\n")

    cases = [
        ("default", [], {}),
        ("--no-color", ["--no-color"], {}),
        ("NO_COLOR=1", [], {"NO_COLOR": "1"}),
    ]
    for name, args, extra_env in cases:
        env = os.environ.copy()
        env.pop("NO_COLOR", None)
        env.update(extra_env)
        command = [
            sys.executable, "-m", "sphinx", "-b", "html", *args,
            str(src), str(Path(tmp) / name),
        ]
        output = subprocess.run(
            command, stdout=subprocess.PIPE, stderr=subprocess.STDOUT, env=env
        ).stdout
        print(f"**** {name} ****", repr(output), sep="\n")

Environment Information

Platform:              win32; (Windows-11-10.0.26200-SP0)
Python version:        3.14.2 (tags/v3.14.2:df79316, Dec  5 2025, 17:18:21) [MSC v.1944 64 bit (AMD64)])
Python implementation: CPython
Sphinx version:        9.1.0
Docutils version:      0.22.4
Jinja2 version:        3.1.6
Pygments version:      2.20.0

Sphinx extensions

Additional context

No response

No source file or test is named. Start by running the provided reproduction script on Windows and compare the output for --no-color and NO_COLOR=1; trace the CLI's terminal-formatting handling and identify the existing tests covering these options. Done means the two mechanisms have consistent ANSI behavior, with regression coverage for the reproduced case.