Initial commit: party-mix-app with prefetch cache, audio preload optimizations

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

apps/backend/Dockerfile

@@ -0,0 +1,15 @@
+FROM golang:1.23-alpine AS builder
+WORKDIR /app
+RUN apk add --no-cache git
+COPY go.mod ./
+ENV GOFLAGS=-mod=mod
+RUN go mod download
+COPY . .
+RUN CGO_ENABLED=0 GOOS=linux go build -ldflags="-s -w" -o server ./main.go
+
+FROM alpine:3.20
+RUN apk add --no-cache ca-certificates tzdata
+WORKDIR /app
+COPY --from=builder /app/server .
+EXPOSE 8080
+CMD ["./server"]