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/test-model-connection.ts

@@ -199,13 +199,16 @@ export async function testModelConnection(
             tools: { ping: PING_TOOL },
             maxOutputTokens: 1024,
             maxRetries: 0,
-            abortSignal: AbortSignal.timeout(TEST_TIMEOUT_MS),
+            // Ends with the request: the user closed the dialog or the page
+            abortSignal: req.signal,
+            timeout: TEST_TIMEOUT_MS,
         })
         let calledTool = false
         let finishReason: string | undefined
         for await (const part of result.fullStream) {
             if (part.type === "error") throw part.error
-            // The timeout ends the stream with an abort part, not an error
+            // The timeout (or the request's end) ends the stream with an
+            // abort part, not an error
             if (part.type === "abort") {
                 const timeout = new Error(
                     `The model did not answer within ${TEST_TIMEOUT_MS / 1000} s.`,
@@ -213,7 +216,9 @@ export async function testModelConnection(
                 timeout.name = "TimeoutError"
                 throw timeout
             }
-            if (part.type === "tool-call") {
+            // A call of a tool that does not exist, or with unreadable
+            // input, arrives marked invalid: no proof of tool support
+            if (part.type === "tool-call" && !part.invalid) {
                 calledTool = true
                 break
             }