docs: update README stable Rust guidance

[konard]

Summary

• Update README installation guidance to use doublets = "0.3.0".
• Replace stale nightly Rust instructions with stable Rust 1.85+ guidance from doublets/Cargo.toml and rust-toolchain.toml.
• Add scripts/check-toolchain-docs.rs and wire it into CI so stale README/toolchain guidance is caught automatically.
• Refresh CONTRIBUTING checks and Cargo.lock package metadata to match the current crate version.

Reproduction

Before the documentation update, the new guard failed with the stale guidance:

rust-script scripts/check-toolchain-docs.rs

It reported the old doublets = "0.1.0-pre" snippet, the nightly Rust requirement, and the old contributing toolchain text.

Validation

• rust-script scripts/check-toolchain-docs.rs
• rust-script scripts/check-readme-badges.rs
• rust-script scripts/check-file-size.rs
• cargo fmt --all -- --check
• cargo clippy --all-targets --all-features
• cargo test --all-features --verbose
• cargo test --doc --verbose
• GITHUB_BASE_REF=main rust-script scripts/check-changelog-fragment.rs
• GITHUB_EVENT_NAME=pull_request GITHUB_HEAD_REF=issue-55-c5a7335ee9a7 GITHUB_BASE_REF=main rust-script scripts/check-version-modification.rs

Fixes #55

[konard]

Working session summary

Implemented and pushed the fix to PR #56: #56

What changed:

• Updated README.md to use doublets = "0.3.0" and stable Rust 1.85+ guidance.
• Updated CONTRIBUTING.md to match the stable toolchain.
• Added scripts/check-toolchain-docs.rs and wired it into CI.
• Added a changelog fragment and refreshed Cargo.lock package metadata to 0.3.0.

Validation:

• Local fmt, clippy, tests, doc tests, docs checks, changelog check, and version-modification check passed.
• GitHub CI passed for commit 94c6aa7: https://github.com/linksplatform/doublets-rs/actions/runs/26665920179
• PR is marked ready for review, merge state is clean, and the working tree is clean.

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[konard]

🤖 Solution Draft Log

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💰 Cost estimation:

• Model: GPT-5.5
• Provider: OpenAI
• Public pricing estimate: $6.329423

📊 Context and tokens usage:

• 97.1K / 1.1M (9%) input tokens, 18.8K / 128K (15%) output tokens

Total: (97.1K + 4.5M cached) input tokens, 18.8K output tokens, $6.329423 cost

🤖 Models used:

• Tool: OpenAI Codex
• Requested: gpt-5.5
• Model: GPT-5.5 (gpt-5.5)

📎 Log file uploaded as Repository (27751KB)

• View complete solution draft log

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[konard]

🎉 Auto-merged

This pull request has been automatically merged by hive-mind.

• All CI checks have passed

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Auto-merged by hive-mind with --auto-merge flag