feat(lychee): add local cache for local runs

[zeitlinger]

What changed

This adds a flint-managed local cache path for lychee to speed up repeated local link checks.

• enable a local lychee cache outside CI when the lychee config does not already set cache = true
• skip the flint-managed cache on CI
• add FLINT_LYCHEE_SKIP_LOCAL_CACHE=true as a local opt-out
• create .lychee_cache/.gitignore on first use and print a one-time notice with the opt-out hint
• keep lychee config resolution working for both project-root-relative and FLINT_CONFIG_DIR-relative paths

Why

Lychee supports a disk cache, but many repos will not have it enabled in their lychee config. Flint already orchestrates lychee behavior, so this lets local runs pick up a cache by default without changing shared repo config that would also affect CI.

Impact

Local lychee runs should get faster after the first run. CI behavior stays unchanged, and repos that already opt into lychee's own cache = true continue to use that instead of flint's local cache wrapper.

Validation

• FLINT_CASES=lychee cargo test cases
• cargo test
• mise run lint:fix

[Copilot]

Pull request overview

Adds a flint-managed local disk cache for lychee during local (non-CI) runs to speed up repeated link checks, with an env-var opt-out and behavior that defers to lychee when caching is already enabled in the user’s lychee.toml.

Changes:

• Enable a local .lychee_cache/ directory + --cache flag outside CI (unless opted out or cache = true is already set in lychee config).
• Adjust lychee config-path resolution to work with both project-root-relative and FLINT_CONFIG_DIR-relative config setups.
• Extend and add case tests to cover cache creation behavior and the “config enables cache” bypass; update docs to describe the new behavior.

Reviewed changes

Copilot reviewed 15 out of 15 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
tests/cases/lychee/local-missing-token-warns/test.toml	Updates expected stderr to include the one-time local cache creation notice.
tests/cases/lychee/local-cache-created/test.toml	New case asserting cache dir creation, .gitignore creation, working dir change, and --cache flag injection.
tests/cases/lychee/local-cache-created/files/README.md	Input file for the new local-cache-created case.
tests/cases/lychee/local-cache-created/files/mise.toml	Tooling fixture for the new local-cache-created case.
tests/cases/lychee/local-cache-created/files/lychee.toml	Lychee config fixture (without cache = true) for the new local-cache-created case.
tests/cases/lychee/config-cache-skips-flint-local-cache/test.toml	New case asserting that cache = true in config prevents flint’s local cache wrapper behavior.
tests/cases/lychee/config-cache-skips-flint-local-cache/files/README.md	Input file for the config-cache-skips case.
tests/cases/lychee/config-cache-skips-flint-local-cache/files/mise.toml	Tooling fixture for the config-cache-skips case.
tests/cases/lychee/config-cache-skips-flint-local-cache/files/lychee.toml	Lychee config fixture enabling cache to exercise the bypass.
tests/cases/lychee/clean/test.toml	Updates expected stderr to include the cache creation notice.
tests/cases/lychee/broken-link/test.toml	Updates expected stderr to include the cache creation notice.
src/registry/checks.rs	Documents the new local-cache behavior in the check registry docs.
src/linters/lychee.rs	Implements cache planning (CI skip, opt-out, config detection), config path resolution, and working-dir/input adjustments.
README.md	Removes inline linter config examples and points readers to docs/linters.md.
docs/linters.md	Documents the new local lychee cache behavior and opt-out env var.

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