chore: rebrand project to GopherGate

Updated all naming from LLM Proxy to GopherGate. Implemented new CSS-based branding and updated Go module/binary naming.

go.mod

@@ -1,4 +1,4 @@
-module llm-proxy
+module gophergate
 
 go 1.26.1
 
@@ -9,6 +9,7 @@ require (
 	github.com/gorilla/websocket v1.5.3
 	github.com/jmoiron/sqlx v1.4.0
 	github.com/joho/godotenv v1.5.1
+	github.com/shirou/gopsutil/v3 v3.24.5
 	github.com/spf13/viper v1.21.0
 	golang.org/x/crypto v0.48.0
 	modernc.org/sqlite v1.47.0
@@ -44,7 +45,6 @@ require (
 	github.com/quic-go/quic-go v0.59.0 // indirect
 	github.com/remyoudompheng/bigfft v0.0.0-20230129092748-24d4a6f8daec // indirect
 	github.com/sagikazarmark/locafero v0.11.0 // indirect
-	github.com/shirou/gopsutil/v3 v3.24.5 // indirect
 	github.com/shoenig/go-m1cpu v0.1.6 // indirect
 	github.com/sourcegraph/conc v0.3.1-0.20240121214520-5f936abd7ae8 // indirect
 	github.com/spf13/afero v1.15.0 // indirect