speed up docker build: bun everywhere, buildx layer cache, tighter dockerignore

Root cause of 6+ min builds: Dockerfile stage 1 ran 'npm install' with no
package-lock.json, so every build re-resolved + re-fetched the full npm tree
from scratch on a fresh runner.

- Dockerfile: replace node:22-slim+npm stage with oven/bun:1-slim; both
  stages now 'bun install --frozen-lockfile' against the tracked bun.lock;
  --mount=type=cache for the bun install cache
- workflow: switch to docker/build-push-action with registry buildcache
  (cache-from + cache-to) so layers persist across runs
- dockerignore: add .worktrees, docs, tests, tsbuildinfo so the build context
  ships less

.dockerignore

@@ -4,6 +4,12 @@ data/
 .git/
 .gitea/
 .claude/
+.worktrees/
+docs/
 .env*
 *.md
 *.xml
+*.tsbuildinfo
+**/__tests__/
+**/*.test.ts
+**/*.test.tsx