[Test] Task service api test fix review

[machichima]

Tracking issue

follow-up: #6823

Why are the changes needed?

Fix remaining reviews in #6823

What changes were proposed in this pull request?

• Fast fail is api test server failed to start
• Improve clean-up logic
• Remove redundant code

How was this patch tested?

• API test

❯ make api-test
Makefile:58: warning: overriding commands for target `test'
../go.Makefile:96: warning: ignoring old commands for target `test'
Makefile:122: warning: overriding commands for target `clean'
../go.Makefile:132: warning: ignoring old commands for target `clean'
Running API integration tests...
# github.com/flyteorg/flyte/v2/runs/test/api.test
ld: warning: '/private/var/folders/27/52rf9wx95tvfqzcw0t_x7qqc0000gn/T/go-link-2876845023/000023.o' has malformed LC_DYSYMTAB, expected 98 undefined symbols to start at index 1626, found 95 undefined symbols starting at index 1626
time="2025-12-30T16:41:17+08:00" level=info msg="Set connection pool values to [{MaxOpenConnections:0 OpenConnections:0 InUse:0 Idle:0 WaitCount:0 WaitDuration:0s MaxIdleClosed:1 MaxIdleTimeClosed:0 MaxLifetimeClosed:0}]"
2025/12/30 16:41:17 Database initialized
time="2025-12-30T16:41:17+08:00" level=info msg="Database migrations completed successfully (recreated actions table)"
2025/12/30 16:41:17 Database migrations completed
2025/12/30 16:41:17 Test server starting on http://localhost:8091
2025/12/30 16:41:17 Test server is ready
=== RUN   TestDeployTask
time="2025-12-30T16:41:17+08:00" level=info msg="Created/Updated task: test-org/test-project/test-domain/test-task version 1767084077691962000"
    task_service_test.go:59: Task deployed successfully: org:"test-org" project:"test-project" domain:"test-domain" name:"test-task" version:"1767084077691962000"
    task_service_test.go:74: Task details retrieved successfully: task_id:{org:"test-org" project:"test-project" domain:"test-domain" name:"test-task" version:"1767084077691962000"} metadata:{short_name:"test-task" deployed_at:{seconds:-62135596800}} spec:{task_template:{type:"container" container:{image:"alpine:latest" args:"echo" args:"hello"}}}
    task_service_test.go:24: Test database cleaned up
--- PASS: TestDeployTask (0.01s)
PASS
2025/12/30 16:41:17 Test server stopped
ok      github.com/flyteorg/flyte/v2/runs/test/api      1.050s

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[machichima]

@yuhuan130 PTAL