Migrate link checking from local scripts to flint

[zeitlinger]

Context

The other OTel Java repos have been migrated to use flint for link checking (consolidated, SHA-pinned mise task) instead of the 3 scripts in .mise/tasks/lint/:

• Use flint for link checking opentelemetry-java-instrumentation#16270 (merged)
• Use flint for link checking opentelemetry-java#8116
• Use flint for link checking opentelemetry-java-examples#1034
• Use flint for link checking opentelemetry-configuration#546
• Use flint for link checking semantic-conventions-java#424

What to do in contrib

Since this repo hosts the original scripts in .mise/tasks/lint/, the migration is slightly different:

1. mise.toml: Replace the local lint:links, lint:local-links, and lint:links-in-modified-files task definitions with a single remote flint task (same as the other repos)
2. .github/workflows/reusable-link-check.yml: Simplify to the flint pattern (env vars + mise run lint:links / mise run lint:links --full)
3. .github/config/lychee.toml: Remove the lychee#1729 remap workaround (flint handles it at runtime)
4. .github/renovate.json5: Add the flint custom manager for automatic SHA bumps
5. .mise/tasks/lint/: Keep markdown.sh (still used). Remove links.sh, local-links.sh, and links-in-modified-files.sh since no repo references them anymore

Note

The shell scripts in .mise/tasks/lint/ should only be removed after the PRs in the other repos are merged, so nothing breaks during the transition.

[zeitlinger]

@trask here's the overview how to continue the flint rollout