Fix startup benchmark tool path construction

[lawrencecchen]

Summary

• move trusted startup benchmark tool path and digest recording into a tested Python helper
• fix the hosted Windows/Linux/macOS failure caused by dividing two strings instead of joining Path values
• run the helper regression test in the benchmark job before the build

Evidence

Red commit 3bb0241000 fails cmux-tui/scripts/tests/test_record_startup_tools.py with the hosted TypeError: unsupported operand type(s) for /: 'str' and 'str'.

Green commit 187dffe3e1 passes the same test and uses separate Path joins for release/examples.

No local Rust, Cargo, Zig, Xcode, or build command was run.

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Summary by cubic

Fixes CI failures in the startup benchmark by moving path construction and digest recording into a tested Python helper. Old behavior used inline workflow Python that divided strings when building paths (TypeError on hosted runners); new behavior uses pathlib.Path, validates tool presence under release/examples, and writes digests to GITHUB_OUTPUT. Side effect: adds a small pre-build test step.

• Replaces the heredoc Python step in .github/workflows/cmux-tui-startup-benchmark.yml with cmux-tui/scripts/record_startup_tools.py.
• Adds cmux-tui/scripts/tests/test_record_startup_tools.py and runs it before the build.
• Helper emits binary_sha256 and supervisor_sha256; supports targets and platform suffixes.
• No change to benchmark semantics; CI is now reliable across Windows, Linux, and macOS.

^{Written for commit 187dffe. Summary will update on new commits.}

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[lawrencecchen]

Superseded by PR #10263, which replays this red/green path fix on the current PR #10238 stack. Closing this duplicate source PR.