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.

hooks/use-diagram-tool-handlers.ts

@@ -1,3 +1,4 @@
+import type { ChatAddToolOutputFunction } from "ai"
 import type { RefObject } from "react"
 import type { DiagramOperation } from "@/components/chat/types"
 import type {
@@ -5,6 +6,7 @@ import type {
     ValidationStatus,
 } from "@/components/chat/ValidationCard"
 import type { LoadMode } from "@/contexts/diagram-context"
+import type { ChatUIMessage } from "@/lib/chat-message"
 import { pageModelXml, pageSelectorFor, placeOnPage } from "@/lib/diagram-pages"
 import type { ValidationResult } from "@/lib/diagram-validator"
 import { formatValidationFeedback } from "@/lib/diagram-validator"
@@ -24,25 +26,8 @@ interface ToolCall {
     input: unknown
 }
 
-type AddToolOutputSuccess = {
-    tool: string
-    toolCallId: string
-    state?: "output-available"
-    output: string
-    errorText?: undefined
-}
-
-type AddToolOutputError = {
-    tool: string
-    toolCallId: string
-    state: "output-error"
-    output?: undefined
-    errorText: string
-}
-
-type AddToolOutputParams = AddToolOutputSuccess | AddToolOutputError
-
-type AddToolOutputFn = (params: AddToolOutputParams) => void
+// useChat's addToolOutput, typed with the chat's tools
+type AddToolOutputFn = ChatAddToolOutputFunction<ChatUIMessage>
 
 const MAX_VALIDATION_RETRIES = 3