[codex] simplify literal logger writes

[bobzhang]

Summary

• Replace simple literal write_string(...) calls with the existing <+ writer/logger sugar.
• Keep interpolated strings, non-literal writes, chained writes, and defer writes unchanged to avoid changing evaluation order or string rendering.
• Covers tests, documentation examples, and small support-code builders.

Validation

• moon fmt
• moon check
• moon test
• moon info

Note: the first moon test pass hit the known timing-sensitive process/cancel_test case; it passed in isolation and the full suite passed on rerun.

[coveralls]

Coverage Report for CI Build 292

Coverage decreased (-0.006%) to 78.276%

Details

• Coverage decreased (-0.006%) from the base build.
• Patch coverage: 3 of 3 lines across 2 files are fully covered (100%).
• No coverage regressions found.

Uncovered Changes

No uncovered changes found.

Coverage Regressions

No coverage regressions found.

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Coverage Stats

Relevant Lines:	4189
Covered Lines:	3279
Line Coverage:	78.28%
Coverage Strength:	59410.67 hits per line

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💛 - Coveralls