llm: route every LLM caller through a shared backend client

Replaces the per-plugin Ollama HTTP calls with internal/llm, which picks a
backend from the environment (vLLM or Ollama) behind one Chat interface, plus
internal/plugin/llm_client.go as the plugin-facing wrapper.

Startup now logs llm_backend/llm_endpoint/llm_model instead of the two
OLLAMA_* vars, which no longer describe where inference actually goes.

These files were already running in prod from the vLLM migration but had never
been committed; this is that live state, byte-for-byte.

internal/plugin/hangman.go

@@ -856,9 +856,7 @@ func (p *HangmanPlugin) handleSubmit(ctx MessageContext, phrase string) error {
 	}
 
 	// LLM screening
-	ollamaHost := os.Getenv("OLLAMA_HOST")
-	ollamaModel := os.Getenv("OLLAMA_MODEL")
-	if ollamaHost == "" || ollamaModel == "" {
+	if !llmConfigured() {
 		// No LLM available — add directly
 		if err := p.addPhrase(phrase); err != nil {
 			if err.Error() == "duplicate phrase" {
@@ -879,7 +877,7 @@ or
 
 Phrase: %s`, phrase)
 
-	result, err := callOllama(ollamaHost, ollamaModel, prompt)
+	result, err := callLLM(prompt)
 	if err != nil {
 		slog.Error("hangman: LLM screening failed", "err", err)
 		// Fail open — add it