ci: update to rust version of flint

[zeitlinger]

This updates the existing link linting to the current Rust-based flint release.

What changes in this PR:

• install flint from github:grafana/flint = "0.20.3"
• replace the old remote lint:links shell task with flint run
• keep the existing Lychee configuration under .github/config
• enable check_all_local = true so local links are checked across the repo
• preserve --full on push and scheduled runs so link checking still scans the full repo outside pull requests

Why this stays small:

• this repo does not currently carry Markdown lint wiring to migrate here
• the goal is only to replace the old link-check task with the released Rust flint path

Verification:

• mise run lint
• mise run lint --full

[zeitlinger]

broke before and is now fixed: Error: https://raw.githubusercontent.com/open-telemetry/opentelemetry-java/main/CONTRIBUTING.md#style-guideline | Cannot find fragment: Fragment not found in document. Check if fragment exists or page structure