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

.gitea/workflows/build.yml

@@ -14,6 +14,9 @@ jobs:
     steps:
       - uses: actions/checkout@v4
 
+      - name: Set up Docker Buildx
+        uses: docker/setup-buildx-action@v3
+
       - name: Log in to Gitea Container Registry
         run: echo "${{ secrets.REGISTRY_TOKEN }}" | docker login "$REGISTRY" -u "${{ github.actor }}" --password-stdin
 
@@ -21,14 +24,13 @@ jobs:
         id: meta
         run: echo "version=$(jq -r .version package.json)" >> "$GITHUB_OUTPUT"
 
-      - name: Build image
-        run: |
-          docker build \
-            -t "$REGISTRY/$IMAGE:latest" \
-            -t "$REGISTRY/$IMAGE:${{ steps.meta.outputs.version }}" \
-            .
-
-      - name: Push image
-        run: |
-          docker push "$REGISTRY/$IMAGE:latest"
-          docker push "$REGISTRY/$IMAGE:${{ steps.meta.outputs.version }}"
+      - name: Build and push
+        uses: docker/build-push-action@v6
+        with:
+          context: .
+          push: true
+          tags: |
+            ${{ env.REGISTRY }}/${{ env.IMAGE }}:latest
+            ${{ env.REGISTRY }}/${{ env.IMAGE }}:${{ steps.meta.outputs.version }}
+          cache-from: type=registry,ref=${{ env.REGISTRY }}/${{ env.IMAGE }}:buildcache
+          cache-to: type=registry,ref=${{ env.REGISTRY }}/${{ env.IMAGE }}:buildcache,mode=max