Fix startup benchmark tool path construction

[lawrencecchen]

Depends on #10238.

This branch replays the red test and green Path-based fix from PR10237 onto the current PR10238 head. The workflow expression trusted_release /= "release" / "examples" evaluates string division before pathlib division and raises TypeError. The helper now constructs release/example paths as Path operands and has a focused behavior test.

Checks: focused path test, cmux-tui SDK/spec checks, startup contract/claim checks. Rust/Cargo/Zig/Xcode builds were not run locally.

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[lawrencecchen]

Closing this stale benchmark-path stack. The referenced startup benchmark files are absent from current main. Recreate the benchmark against the current runner contract when the measurement target is defined.