docs: refresh public contributing guide

[LouisDeconinck]

Summary

Refresh the public contributing page to match the first-15-minutes onboarding guidance from Dagu #2569.

Changes

• Add track-based first-change guidance for docs, UI, executor, and API/CLI work.
• Document package-scoped validation and the docs-only Go-toolchain exemption.
• Use the current make run-server UI development loop and focused PR checklist.

Related issue

• docs: make first-time contributing less overwhelming dagu#2569

Checks

• pnpm build
• pnpm test:worker
• git diff --check

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Summary by cubic

Refreshes the public contributing guide to match the first-15-minutes onboarding flow so new contributors can make their first change faster.

• Adds track-based first-change guidance for docs, UI, executor, and API/CLI work.
• Documents package-scoped validation commands and the docs-only Go-toolchain exemption.
• Replaces the old prerequisites and make instructions with the current make run-server loop and a focused PR checklist.
• Connects the updated flow to the onboarding guidance from docs: make first-time contributing less overwhelming dagu#2569.

^{Written for commit bfc1e32. Summary will update on new commits.}

[coderabbitai]

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