perf: optimize Docker images - backend 294MB, gateway 1.89GB

Backend:
- node:22-alpine runtime (from 1.82GB to 294MB, 84% reduction)
- COPY --chown instead of chown -R layer
- pnpm install --prod after build for clean .pnpm store
- Pinned pnpm@10 to avoid v11 build-script lockout

Gateway:
- Fixed TypeScript errors (missing table defs in shared schema)
- Restored node-crc Rust patch for native compilation
- Multi-stage build with COPY --chown
- pnpm install --prod after build
- ffmpeg with --no-install-recommends

Proxy:
- Restructured for standalone build (build errors are pre-existing)

General:
- pnpm@10 in all builds (avoids ERR_PNPM_IGNORED_BUILDS)
- Clean .dockerignore (excludes docs/design/scripts)

services/discord-gateway/patches/node-crc@4.0.0.patch

@@ -0,0 +1,13 @@
+diff --git a/Cargo.toml b/Cargo.toml
+index a967508960d8b6b686b23401ea14333b858a675c..d0282a30ee931563a65d774ed783c83d6d2fdd5e 100644
+--- a/Cargo.toml
++++ b/Cargo.toml
+@@ -3,7 +3,7 @@ name = "node-crc"
+ version = "4.0.0"
+ authors = ["Magic Len <len@magiclen.org>"]
+ edition = "2021"
+-rust-version = "1.65"
++rust-version = "1.77.0"
+ repository = "https://github.com/magiclen/node-crc"
+ homepage = "https://magiclen.org/node-js-crc/"
+ keywords = ["nodejs", "crc8", "crc16", "crc32", "crc64"]