KAFKA-7493: Remove obsolete controller bounce-at-start Streams test

[majialoong]

Since the classic broker controller is gone, this PR removes the ignored test_broker_type_bounce_at_start from streams_broker_bounce_test.py.
It also thins out the remaining test code by removing the obsolete broker_type parameter path and the sleep_time_secs == 0 startup-failure handling logic.

[majialoong]

Tested locally with TC_PATHS="tests/kafkatest/tests/streams/streams_broker_bounce_test.py" bash tests/docker/run_tests.sh

================================================================================
SESSION REPORT (ALL TESTS)
ducktape version: 0.14.0
session_id:       2026-05-31--001
run time:         164 minutes 17.242 seconds
tests run:        28
passed:           28
flaky:            0
failed:           0
ignored:          0
================================================================================