Add LLM busy modes: wait (hang) or reject with Retry-After

LLM_BUSY_MODE=reject answers blocked LLM requests immediately with
LLM_BUSY_STATUS (default 503, 429 works) and Retry-After, so routers
like LiteLLM can cool down and retry instead of holding a hung
connection. The default wait mode now also sends Retry-After when
LLM_WAIT_TIMEOUT expires. Document the service account (LocalSystem
default, NT SERVICE virtual-account hardening) and the Program
Files / ProgramData install layout.

internal/lock/lock.go

@@ -74,6 +74,22 @@ func (l *Lock) AcquireLLM(ctx context.Context) error {
 	return nil
 }
 
+// TryAcquireLLM acquires one in-flight LLM slot without waiting and
+// reports whether it succeeded. It fails when an image job is active or
+// pending.
+func (l *Lock) TryAcquireLLM() bool {
+	l.mu.Lock()
+	if l.imageActive || len(l.imageQ) > 0 {
+		l.mu.Unlock()
+		return false
+	}
+	l.n++
+	n := l.n
+	l.mu.Unlock()
+	l.logTransition("lock transition", "state", StateLLM, "llm_inflight", n)
+	return true
+}
+
 // ReleaseLLM marks one LLM request as finished.
 func (l *Lock) ReleaseLLM() {
 	l.mu.Lock()

internal/lock/try_test.go

@@ -0,0 +1,51 @@
+package lock
+
+import (
+	"context"
+	"testing"
+	"time"
+)
+
+func TestTryAcquireLLM(t *testing.T) {
+	lk := New(nil)
+	if !lk.TryAcquireLLM() {
+		t.Fatal("TryAcquireLLM on idle lock should succeed")
+	}
+	if _, n, _ := lk.Snapshot(); n != 1 {
+		t.Fatalf("n = %d, want 1", n)
+	}
+
+	// While an image job is pending, TryAcquireLLM must fail.
+	imageWaiting := make(chan struct{})
+	go func() {
+		lk.AcquireImage(context.Background())
+		close(imageWaiting)
+	}()
+	deadline := time.Now().Add(2 * time.Second)
+	for {
+		lk.mu.Lock()
+		queued := len(lk.imageQ)
+		lk.mu.Unlock()
+		if queued == 1 {
+			break
+		}
+		if time.Now().After(deadline) {
+			t.Fatal("image waiter never queued")
+		}
+		time.Sleep(time.Millisecond)
+	}
+	if lk.TryAcquireLLM() {
+		t.Fatal("TryAcquireLLM with image pending should fail")
+	}
+
+	lk.ReleaseLLM()
+	<-imageWaiting
+	if lk.TryAcquireLLM() {
+		t.Fatal("TryAcquireLLM with image active should fail")
+	}
+	lk.ReleaseImage()
+	if !lk.TryAcquireLLM() {
+		t.Fatal("TryAcquireLLM after image release should succeed")
+	}
+	lk.ReleaseLLM()
+}