Fix flaky test ExtensibleLoadManagerTest.startBroker (#21875)

[leocavalhere6]

Fixes #21875

Main Issue: #21875

Motivation

The integration test ExtensibleLoadManagerTest.startBroker was flaky due to a timeout
when waiting for all brokers to become active and for topics to be created and looked up.
This caused intermittent CI failures.

Modifications

• Increased Awaitility timeout from 120s to 4 minutes.
• Separated broker readiness check from topic creation and lookup.
• Ensured all brokers are active before creating partitioned topics.
• Retained original logic for topic creation and lookup without affecting existing tests.

Verifying this change

• Verified locally: the flaky test now consistently passes.
• No new tests added; existing integration tests cover the modified logic.

Does this pull request potentially affect one of the following parts

• Dependencies
• Public API
• Schema
• Default configuration values
• Threading model
• Binary protocol
• REST endpoints
• Admin CLI options
• Metrics
• Deployment

Documentation

• doc
• doc-required
• doc-not-needed
• doc-complete

Matching PR in forked repository

PR in forked repository: N/A

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