Problem

Test_TaskSend/PausedDuringWaitForReady flakes on macOS CI with:

task entered unknown state while waiting for it to become idle

Two prior fixes (PR #25648, PR #25811) added quartz mock clocks and
traps. The flake recurred on CI run 26634123539 (includes both fixes).

Root cause

The quartz resetTrap was released immediately after catching
ticker.Reset (line 174 of task_send.go), then closed. This allowed
client.TaskByID (line 175, one line later) to race with the test's
subsequent DB mutation (pauseTask / PatchAppStatus).

CI log evidence (run 26634123539, post-both-prior-fixes):

11:25:29.643707  GET  /tasks/me/<id>   took=116ms  (poll's TaskByID)
11:25:29.643763  POST /tasks/.../pause took=29ms   (test's pauseTask)

The GET and POST started 56us apart. The poll's 116ms DB query
straddled the stop build's commit, seeing (stop, pending) which the
tasks_with_status view maps to unknown.

WaitsForWorkingAppState has the same structural race (release trap,
then mutate, then advance), though its race is benign since an early
mutation still makes the command succeed.

Fix

Test-only. Both PausedDuringWaitForReady and sibling
WaitsForWorkingAppState are fixed with the same pattern:

1. Keep the resetTrap open across both poll iterations (do not
   close after the first poll)
2. First poll: advance clock, trap catches ticker.Reset freezing the
   goroutine, release immediately. Goroutine proceeds to
   client.TaskByID, sees initial state ("initializing" / "working"),
   continues polling
3. Second poll: advance clock, trap catches ticker.Reset again,
   goroutine is frozen before client.TaskByID
4. Mutate state while goroutine is frozen (pauseTask /
   PatchAppStatus). The DB mutation completes with no concurrent
   reader
5. Release the trap. Goroutine unfreezes, client.TaskByID
   deterministically sees the mutated state
6. Close the trap

No race because the goroutine cannot execute client.TaskByID while
trapped at ticker.Reset.

$ go test -run 'Test_TaskSend/(PausedDuringWaitForReady|WaitsForWorkingAppState)' -v ./cli/
--- PASS: Test_TaskSend/PausedDuringWaitForReady (2.31s)
--- PASS: Test_TaskSend/WaitsForWorkingAppState (7.29s)
PASS

$ go test -run 'Test_TaskSend' -race -count=3 ./cli/ -timeout 300s
ok  cli  58.070s

> [Breakpoint 1] waitForTaskIdle() ./cli/task_send.go:174
=> 174:   ticker.Reset(pollInterval, "task_send", "poll")
   175:   task, err := client.TaskByID(ctx, task.ID)
(dlv) task.Status = "initializing"

    Mock Clock - Ticker.Reset(5s, [task_send poll]) call, matched 1 traps

> [Breakpoint 2] waitForTaskIdle() ./cli/task_send.go:175
=> 175:   task, err := client.TaskByID(ctx, task.ID)
(dlv) task.Status = "initializing"

POST /tasks/.../pause  start="12:31:30.830"  took=111ms
GET  /tasks/me/<id>    start="12:31:30.832"  took=118ms

Closes CODAGT-482

🤖 This PR was created with the help of Coder Agents, and will be reviewed by a human. 🏂🏻