test: Add t.Cleanup() to fix TestEventHandler

[HankStat]

Which issue(s) does the PR fix:

Fixes #57144

Problem

The TestEventHandler test is flaky due to a race condition that causes a "directory not empty" error during cleanup.
When the test completes, the Go testing framework's os.RemoveAll command on the temporary directory races against the App's shutdown process. The test fails if the directory removal attempt occurs before the App has fully closed its file handles.

Solution

Inside the startApp function, I add app.Close() with t.Cleanup().
The Go testing framework guarantees that cleanup functions are executed after a test completes but before temporary directories are removed. This change ensures that the app fully closes and releases all file handles before the directory is deleted, which eliminates the race condition.

Verification

The test now correctly and consistently passes on my local machine after running it 100 times using a loop to simulate the flaky behavior. In addition, after running 100 times, the TestEventHandler test took an average of 1.18 seconds to finish.

cd integrations/event-handler 
go test -v -race . -run ^TestEventHandler$ -count=100

[github-actions]

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[HankStat]

I have read the CLA Document and I hereby sign the CLA

[rosstimothy]

Thanks for attempting to help us improve out tests! I'm however still seeing the same failures reported in the linked issue with this branch using the following command to run the test in a limited environment.

$ cd integrations/event-handler
$ go test -c -race

$ docker run --cpus="0.35" -v/teleport:/teleport golang:1.25.3-bookworm /teleport/integrations/event-handler/event-handler.test -test.count=10000 -test.timeout=120m -test.failfast  -test.run "TestEventHandler"

[rosstimothy]

Can we remove this log line to reduce noise.

Suggested change

t.Log("Close the app...")