Emit the "Integration tests" status check the ruleset requires

[Ilyes512]

Goal

.github/rulesets/Main.json lists "Integration tests" as a required status check, but no job
in .github/workflows/ci.yml ever emits a check by that name. Every pull request to main
therefore waits indefinitely on a check that cannot report, and nothing can merge.

While fixing this, a second broken required check turned up: markdownlint-cli2 only recognises
.markdownlint-cli2.yaml, and the repository had .markdownlint-cli2.yml. The config was never
loaded, the tool exited with a usage error instead of linting, and the required "Markdown gate"
check failed with it.

Scope

• Add an integration-tests job to ci.yml named exactly Integration tests
• Run go test -race -count=1 -tags=integration ./... — the same tag Taskfile.dist.yml
  already passes. A green no-op until integration tests exist is the correct outcome
• Rename .markdownlint-cli2.yml to .markdownlint-cli2.yaml so the config loads (this also
  makes the paths-filter in md.yml, which already referenced .yaml, match reality)
• Fix the markdown errors that surfaced once linting actually ran

Tests

Open a pull request and confirm all three required checks report: "Unit tests",
"Integration tests", "Markdown gate". task md:check should print 0 issues rather than a
usage error.

Depends on

Nothing. Parallel-safe — and it blocks every merge, so it goes first.

Fixed by #1, which is open and waiting on CI. This issue exists so the defect is recorded
against the ruleset rather than buried in a PR description.

Done when

task lint and task test pass, every box above is ticked, and the change ships with its tests and documentation in the same PR (per AGENTS.md).