fix(chat): use the AI SDK's own mechanisms for quota, retries, stops and notices

Server
- Record quota tokens in onStepFinish and await the write, so a step that
  fails or is stopped later still counts; drop the onFinish/onAbort copies
- validate-diagram and the connection test end their model call with the
  request (req.signal) and use the SDK's timeout option; validate-diagram
  reports to Langfuse (functionId "validate-diagram")
- The connection test no longer counts an invalid tool call as support
- Validate incoming messages with safeValidateUIMessages (400 otherwise),
  drop client system messages explicitly, prune empty model messages with
  pruneMessages
- Chat tools move to lib/chat-tools.ts with an output schema for the
  client-side tools

Client
- Every automatic retry sends the canvas as it is then
  (prepareSendMessagesRequest): a drawing is committed before its
  screenshot check can fail, so the model must go on from it
- A notice when the output budget ran out before any tool call
  (finishReason "length")
- Error notices are assistant messages with a data-notice part instead of
  role "system" messages (lib/chat-message.ts: ChatUIMessage with metadata,
  data part and InferUITools types)
- regenerate, edit and retry use sendMessage({ messageId }); isResending
  and flushSync go
- isToolUIPart/getToolName instead of slicing "tool-"; ToolPartLike derives
  from the SDK's part types; addToolOutput typed with ChatAddToolOutputFunction

Tests: step failure after a finished step, abort of the screenshot check,
invalid tool call in the connection test, malformed messages.

lib/chat-message.ts

@@ -0,0 +1,44 @@
+import type { InferUITools, UIMessage } from "ai"
+import type { chatTools } from "@/lib/chat-tools"
+import type { SelectedCell } from "@/stores/canvas-store"
+
+/** Shapes sent with a user message (also kept in its metadata) */
+export type MessageSelection = Pick<SelectedCell, "id" | "label">[]
+
+export interface ChatMessageMetadata {
+    selectedCells?: MessageSelection
+}
+
+/**
+ * A failed request or an answer that drew nothing, shown in the chat with
+ * what to do: an assistant message with this as its only part. The server
+ * ignores data parts, so it never reaches the model.
+ */
+export interface ChatNotice {
+    text: string
+    /** Show a button that opens model settings, on the provider that refused */
+    openModelConfig?: boolean
+    providerId?: string
+}
+
+export type ChatToolName = keyof InferUITools<typeof chatTools>
+
+export type ChatUIMessage = UIMessage<
+    ChatMessageMetadata,
+    { notice: ChatNotice },
+    InferUITools<typeof chatTools>
+>
+
+export function noticeMessage(notice: ChatNotice): ChatUIMessage {
+    return {
+        id: `notice-${Date.now()}`,
+        role: "assistant",
+        parts: [{ type: "data-notice", data: notice }],
+    }
+}
+
+/** The notice a message carries, if it is one */
+export function noticeOf(message: ChatUIMessage): ChatNotice | undefined {
+    const part = message.parts.find((p) => p.type === "data-notice")
+    return part?.data
+}