fix(docker): upgrade all Dockerfiles to node:22-alpine for pnpm v10 compatibility

pnpm v10+ requires the built-in `node:sqlite` module which is only available
in Node 22+. All services now use node:22-alpine.

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

infra/docker/Dockerfile.backend

@@ -1,4 +1,4 @@
-FROM node:20-alpine
+FROM node:22-alpine
 
 WORKDIR /app
 

infra/docker/Dockerfile.discord-gateway

@@ -1,4 +1,4 @@
-FROM node:20-alpine
+FROM node:22-alpine
 
 WORKDIR /app
 

infra/docker/Dockerfile.frontend

@@ -1,4 +1,4 @@
-FROM node:20-alpine
+FROM node:22-alpine
 
 WORKDIR /app