fix(build-arena): disable Claude Code auto-updater in Docker images

Add DISABLE_AUTOUPDATER=1 environment variable to both elide-builder
and standard-builder Dockerfiles to prevent Claude Code from attempting
to auto-update during container builds. This ensures consistent behavior
and prevents potential issues with version drift.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <[email protected]>

Author: rjwalters

tools/build-arena/docker/elide-builder.Dockerfile

@@ -48,6 +48,8 @@ RUN java -version && \
 # Set environment variables
 ENV TERM=xterm-256color
 ENV LANG=C.UTF-8
+# Disable Claude Code auto-update (correct env var from docs)
+ENV DISABLE_AUTOUPDATER=1
 
 # Create non-root user for Claude Code (won't run with --dangerously-skip-permissions as root)
 # Note: Ubuntu 24.04 (Noble) already has UID 1000, so we use the next available UID

tools/build-arena/docker/standard-builder.Dockerfile

@@ -55,6 +55,8 @@ RUN java -version && \
 # Set environment variables
 ENV TERM=xterm-256color
 ENV LANG=C.UTF-8
+# Disable Claude Code auto-update (correct env var from docs)
+ENV DISABLE_AUTOUPDATER=1
 
 # Create non-root user for Claude Code
 # Note: Ubuntu 24.04 (Noble) already has UID 1000, so we use the next available UID