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.

Dockerfile

@@ -9,10 +9,10 @@ RUN go mod download
 COPY . .
 RUN go tool gotailwind -i assets/css/input.css -o assets/css/output.css --minify
 RUN --mount=type=cache,target=/root/.cache/go-build \
-    CGO_ENABLED=0 go build -ldflags="-s" -o /bin/c4 .
-RUN upx -9 -k /bin/c4
+    CGO_ENABLED=0 go build -ldflags="-s" -o /bin/games .
+RUN upx -9 -k /bin/games
 
 FROM scratch
 ENV PORT=8080
-COPY --from=build /bin/c4 /
-ENTRYPOINT ["/c4"]
+COPY --from=build /bin/games /
+ENTRYPOINT ["/games"]