fix: raise the output budget so reasoning models reach the tool call

A reasoning model spends the output budget in order: thinking first, then prose,
then the tool call. With 16000 the thinking alone can consume all of it, so the
turn ends with finishReason "length" before display_diagram is ever called. The
canvas stays empty and nothing surfaces in the UI, because no tool call means no
tool error, and the client never reads finishReason.

Measured on openrouter deepseek/deepseek-v4-flash, the model from the report:
- max_tokens=800 with reasoning on returns reasoning_tokens=800, empty content,
  finish_reason length. So reasoning is billed against this budget, not exempt.
- refining an existing diagram (19k chars of XML in the input) produced 49142
  chars of reasoning, zero tool calls, finishReason "length" at 16000
- the same request at 40000 finished and called edit_diagram with 12 operations

64000 cannot just be sent to every model: bedrock claude-3-haiku caps at 4096,
nova-lite at 10000, and the openrouter deepseek-r1 endpoint counts input and
output against one 64000 ceiling. All three name the real limit in the 400, so
parse it and retry once. Verified: nova-lite logs "64000 rejected, retrying with
10000" and then completes its tool call.

Also expose the budget in Settings. It is sent as a header rather than read from
env only, so desktop users can raise it themselves without an env file.

vercel.json goes back to the 300s it had before #238 traded it for $2-4/month.
That is now Vercel's own default, and billing pauses while the function waits on
the model, so the saving that motivated 120s no longer applies. edgeone.json is
left alone: its 120 may be that platform's actual ceiling.

components/chat-panel.tsx

@@ -178,6 +178,7 @@ export default function ChatPanel({
     const [minimalStyle, setMinimalStyle] = useState(false)
     const [vlmValidationEnabled, setVlmValidationEnabled] = useState(false)
     const [customSystemMessage, setCustomSystemMessage] = useState("")
+    const [maxOutputTokens, setMaxOutputTokens] = useState("")
     const [shouldFocusInput, setShouldFocusInput] = useState(false)
 
     // Restore input from sessionStorage on mount (when ChatPanel remounts due to key change)
@@ -204,6 +205,14 @@ export default function ChatPanel({
         }
     }, [])
 
+    // Load output token budget from localStorage on mount
+    useEffect(() => {
+        const stored = localStorage.getItem(STORAGE_KEYS.maxOutputTokens)
+        if (stored !== null) {
+            setMaxOutputTokens(stored)
+        }
+    }, [])
+
     // Check config on mount
     useEffect(() => {
         fetch(getApiEndpoint("/api/config"))
@@ -320,6 +329,13 @@ export default function ChatPanel({
         localStorage.setItem(STORAGE_KEYS.customSystemMessage, value)
     }, [])
 
+    // Handler for output token budget change (empty string = use server default)
+    const handleMaxOutputTokensChange = useCallback((value: string) => {
+        const digitsOnly = value.replace(/\D/g, "")
+        setMaxOutputTokens(digitsOnly)
+        localStorage.setItem(STORAGE_KEYS.maxOutputTokens, digitsOnly)
+    }, [])
+
     // Ref to store the sendMessage function for use in callbacks
     const sendMessageRef = useRef<typeof sendMessage | null>(null)
 
@@ -1104,6 +1120,9 @@ export default function ChatPanel({
                     ...(minimalStyle && {
                         "x-minimal-style": "true",
                     }),
+                    ...(maxOutputTokens && {
+                        "x-max-output-tokens": maxOutputTokens,
+                    }),
                 },
             },
         )
@@ -1448,6 +1467,8 @@ export default function ChatPanel({
                 onVlmValidationChange={handleVlmValidationChange}
                 customSystemMessage={customSystemMessage}
                 onCustomSystemMessageChange={handleCustomSystemMessageChange}
+                maxOutputTokens={maxOutputTokens}
+                onMaxOutputTokensChange={handleMaxOutputTokensChange}
                 onOpenModelConfig={() => setShowModelConfigDialog(true)}
             />
 

components/settings-dialog.tsx

@@ -75,6 +75,8 @@ interface SettingsDialogProps {
     onOpenModelConfig?: () => void
     customSystemMessage?: string
     onCustomSystemMessageChange?: (value: string) => void
+    maxOutputTokens?: string
+    onMaxOutputTokensChange?: (value: string) => void
 }
 
 export const STORAGE_ACCESS_CODE_KEY = "next-ai-draw-io-access-code"
@@ -101,6 +103,8 @@ function SettingsContent({
     onOpenModelConfig,
     customSystemMessage = "",
     onCustomSystemMessageChange = () => {},
+    maxOutputTokens = "",
+    onMaxOutputTokensChange = () => {},
 }: SettingsDialogProps) {
     const dict = useDictionary()
     const router = useRouter()
@@ -591,6 +595,24 @@ function SettingsContent({
                         />
                     </div>
 
+                    {/* Max Output Tokens */}
+                    <SettingItem
+                        label={dict.settings.maxOutputTokens}
+                        description={dict.settings.maxOutputTokensDescription}
+                    >
+                        <Input
+                            id="max-output-tokens"
+                            type="text"
+                            inputMode="numeric"
+                            value={maxOutputTokens}
+                            onChange={(e) =>
+                                onMaxOutputTokensChange(e.target.value)
+                            }
+                            placeholder="64000"
+                            className="h-9 w-28 text-sm"
+                        />
+                    </SettingItem>
+
                     {/* Send Shortcut */}
                     <SettingItem
                         label={dict.settings.sendShortcut}