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.

tests/unit/validate-model-route.test.ts

@@ -141,6 +141,24 @@ describe("POST /api/validate-model", () => {
         expect(data.valid).toBe(true)
         expect(data.warning).toMatch(/without calling a tool/)
     })
+
+    it("warns when the model calls a tool that does not exist", async () => {
+        // The SDK passes the call on, marked invalid
+        streamReply({
+            role: "assistant",
+            tool_calls: [
+                {
+                    index: 0,
+                    id: "call_1",
+                    type: "function",
+                    function: { name: "pong", arguments: "{}" },
+                },
+            ],
+        })
+        const data = await testGlm()
+        expect(data.valid).toBe(true)
+        expect(data.warning).toMatch(/without calling a tool/)
+    })
 })
 
 describe("chat requests to a client base URL", () => {