`/feedback` uploads can include `codex-logs.log` from the in-memory
feedback logger path. That logger was emitting level + message without a
timestamp, which made some uploaded logs much harder to inspect. This
change makes the feedback logger use an explicit timer so
feedback-captured log lines include timestamps consistently.
This is not Windows-specific code. The bug showed up in Windows reports
because those uploads were hitting the feedback-buffer path more often,
while Linux/macOS reports were typically coming from the SQLite feedback
export, which already prefixes timestamps.
Here's an example of a log that is missing the timestamps:
```
TRACE app-server request: getAuthStatus
TRACE app-server request: model/list
INFO models cache: evaluating cache eligibility
INFO models cache: attempting load_fresh
INFO models cache: loaded cache file
INFO models cache: cache version mismatch
INFO models cache: no usable cache entry
DEBUG
INFO models cache: cache miss, fetching remote models
TRACE windows::current_platform is called
TRACE Returning Info { os_type: Windows, version: Semantic(10, 0, 26200), edition: Some("Windows 11 Professional"), codename: None, bitness: X64, architecture: Some("x86_64") }
```
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