test(coderd): make the chatd idle wait fail on timeout - #30967

chatd.WaitUntilIdleForTest waited up to 10 seconds for the chat worker to go idle, dropped the timeout error, and then drained tracked work, so a test whose worker never went idle passed after a silent 10-second stall. The hook now takes the caller's ctx and returns an error when ctx ends before the worker is idle or the tracked work finishes. Its 26 callers wrap it in require.NoError. The poll loop moves from chatWorker.WaitIdle, whose only caller was the hook, into testhooks.go. It polls on a real 10 ms ticker instead of the server clock, which a mock clock never advances.

Why it is safe

• The idle check is unchanged: the hook reads the runner manager under the worker's lock and returns at once when the worker or manager is nil. The drain still calls drainInflight, now in a goroutine so that ctx bounds it; that goroutine exits once Close cancels the tracked work.
• Red-green for the idle wait: with runnerManager.idle forced to return false, TestCreateChatImmediatelyProcessesNewChat passes on main after 10.2 s and fails on this branch at its 25 s context with wait for the chat worker to go idle: context deadline exceeded.
• Red-green for the drain: a probe that holds one tracked task open stayed blocked in the hook 2 s past a 100 ms context on this PR's first head, then returned nil. It now returns wait for tracked chat work to finish: context deadline exceeded at 100 ms.
• Hidden timeouts: on main, with the hook instrumented to report errors and idle waits over 1 s, all 119 hook calls in the packages below returned in under 1 s without an error. The runs below pass with the bounded drain, so no test needed a fix.
• git grep WaitIdle finds no other caller.

Review focus

Callers now pass their own test context instead of getting a fresh 10 s one. Every direct caller, and every caller of coderdtest.WaitForChatSettled and waitForChatProcessed, passes a context of testutil.WaitLong or longer, so the budget grows, but the rest of the test shares it.

The goroutine around the drain adds 9 lines, so this PR adds 7 more lines than it removes. Without it, a stalled title or summary call holds the hook past its deadline.

Validation

• go test ./coderd/x/chatd/ -count=3: pass.
• go test ./coderd/ -count=3 -run '<every test in exp_chats_test.go, exp_chats_workspace_file_test.go, and exp_chats_hooks_test.go>': pass.
• go test ./codersdk/toolsdk/ -count=3 -run '^(TestChatTools|TestCreateChatOrganizationDefaultModel)$': pass.
• The mutant and the probe use go test -overlay; a copy with a syntax error fails to build, so the overlay applies.
• The pre-commit hook (make pre-commit) passed.

Xum, an AI agent, opened this PR for @ibetitsmike and wrote this description.