ci: build against bread-ecosystem's shared Arch CI image, add check.yml

Same fix as breadpad: build inside the shared pinned Arch container
(bread-ecosystem/ci/, cloned at the sha in ci/bread-ecosystem.rev)
instead of building natively against whatever's on the runner host.
Adds check.yml (clippy + test on feature/**/fix/**) as a fast-fail gate
before anything reaches main.

Verified locally: build, clippy, and test all pass through the new
container path — no pre-existing lint/test debt found here.

ci/build.sh

@@ -0,0 +1,20 @@
+#!/usr/bin/env bash
+# Delegates to bread-ecosystem's shared CI build image/script, pinned to
+# the commit in ci/bread-ecosystem.rev — not `main`. bread-ecosystem's CI
+# files now affect every product's release pipeline, so bumping the pin
+# is a deliberate act instead of silent drift.
+#
+# Usage: ci/build.sh cargo build --release --locked
+set -euo pipefail
+
+ROOT="$(cd "$(dirname "${BASH_SOURCE[0]}")/.." && pwd)"
+REV="$(cat "${ROOT}/ci/bread-ecosystem.rev")"
+
+CACHE_DIR="/tmp/bread-ecosystem-ci-${REV}"
+if [ ! -d "$CACHE_DIR" ]; then
+    rm -rf /tmp/bread-ecosystem-ci-*
+    git clone https://git.breadway.dev/Breadway/bread-ecosystem.git "$CACHE_DIR"
+    git -C "$CACHE_DIR" checkout --quiet "$REV"
+fi
+
+bash "${CACHE_DIR}/ci/build.sh" breadclip "$ROOT" "$@"