**Which issue(s) this PR fixes**:
Fixes #

**What this PR does / why we need it**:
Gating the read loop on `process_exist?(pid)` is racy: fluentd can write
its final error line and exit right after `eager_read` drains the pipe,
so the loop exits (process gone) before that last line is read. The
error message is then missing from `stdio_buf` and the assertion fails
even though fluentd did fail to start as expected.

This showed up as a flaky failure of "fails to launch fluentd if
specified root path is invalid path for directory": the captured output
ended at "bundler: failed to load command:" without the following "non
directory entry exists:" line.

Loop until the pipe reaches EOF (the write-end is closed when the
process exits) instead, so the remaining buffered output is always
drained. The success case still breaks early once the worker is running,
and hangs are still caught by the outer `waiting(timeout)`. This mirrors
the existing EOF handling in `assert_log_matches`.

This PR will fix following error:
```
4) Failure: test: fails to launch fluentd if specified root path is invalid path for directory(TestFluentdCommand::with system configuration about root directory):
  fluentd failed to start, without specified regular expressions:
  2026-07-19 09:09:44 +0000 [info]: init supervisor logger path=nil rotate_age=nil rotate_size=nil
  2026-07-19 09:09:44 +0000 [info]: parsing config file is succeeded path="/Users/runner/work/fluentd/fluentd/test/command/../tmp/commandfluentd/ce6c61934634f7909ab7/existing_root_dir.conf"
  2026-07-19 09:09:44 +0000 [info]: inaccessible include directory was specified path="/etc/fluent/conf.d"
  2026-07-19 09:09:44 +0000 [info]: gem 'fluentd' version '1.19.0'
  bundler: failed to load command: /Users/runner/work/fluentd/fluentd/bin/fluentd (/Users/runner/work/fluentd/fluentd/bin/fluentd)
  .
  <false> is not true.
/Users/runner/work/fluentd/fluentd/test/command/test_fluentd.rb:271:in `assert_fluentd_fails_to_start'
/Users/runner/work/fluentd/fluentd/test/command/test_fluentd.rb:378:in `block (2 levels) in <class:TestFluentdCommand>'
     375:       end
     376:       conf_path = create_conf_file('existing_root_dir.conf', @conf)
     377:
  => 378:       assert_fluentd_fails_to_start(
     379:         create_cmdline(conf_path),
     380:         "non directory entry exists:#{@root_path}",
     381:       )
```
Ref.
https://github.com/fluent/fluentd/actions/runs/29680404414/job/88175417915?pr=5446#step:6:5364

**Docs Changes**:
N/A

**Release Note**:
N/A

Signed-off-by: Shizuo Fujita <fujita@clear-code.com>
Signed-off-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>