refactor: rename remaining c4 references to games

Update binary name, DB path, session cookie, deploy scripts, systemd
service, Docker config, CI workflow, and .dockerignore. Remove stale
Claude command and settings files.

deploy/deploy.sh

@@ -1,11 +1,11 @@
 #!/usr/bin/env bash
-# Deploy the c4 binary to /opt/c4, then restart the service.
+# Deploy the games binary to /opt/games, then restart the service.
 # Works from the repo (builds first) or from an extracted tarball (pre-built binary).
 set -euo pipefail
 
 ROOT_DIR="$(cd "$(dirname "$0")/.." && pwd)"
-INSTALL_DIR="/opt/c4"
-BINARY="$ROOT_DIR/c4"
+INSTALL_DIR="/opt/games"
+BINARY="$ROOT_DIR/games"
 
 # If Go is available and we have source, build fresh
 if [[ -f "$ROOT_DIR/go.mod" ]] && command -v go &>/dev/null; then
@@ -13,7 +13,7 @@ if [[ -f "$ROOT_DIR/go.mod" ]] && command -v go &>/dev/null; then
   (cd "$ROOT_DIR" && go tool gotailwind -i assets/css/input.css -o assets/css/output.css --minify)
 
   echo "Building binary..."
-  (cd "$ROOT_DIR" && CGO_ENABLED=0 go build -o c4 .)
+  (cd "$ROOT_DIR" && CGO_ENABLED=0 go build -o games .)
 fi
 
 if [[ ! -f "$BINARY" ]]; then
@@ -22,10 +22,10 @@ if [[ ! -f "$BINARY" ]]; then
 fi
 
 echo "Installing to $INSTALL_DIR..."
-install -o games -g games -m 755 "$BINARY" "$INSTALL_DIR/c4"
+install -o games -g games -m 755 "$BINARY" "$INSTALL_DIR/games"
 
 echo "Restarting service..."
-systemctl restart c4.service
+systemctl restart games.service
 
 echo "Done. Status:"
-systemctl status c4.service --no-pager
+systemctl status games.service --no-pager