processor: fix a bug that will cause processor Tick get stuck when downstream is Kafka (#11339)

[ti-chi-bot]

This is an automated cherry-pick of #11339

What problem does this PR solve?

Issue Number: close #11340

What is changed and how it works?

Check List

Tests

• Unit test
• Manual test (add detailed scripts or steps below)

Deploy a cdc cluster, create two changefeeds and synchronize the same table to both Kafka and TiDB separately.

Every 20 minutes, inject CDC to network isolation:

• First, isolate cdc to Kafka network for 10 minutes.
• Then, 20 minutes later, isolate cdc to downstream TiDB network for 10 minutes.

Repeat this process six times.

Before this PR, the lag in the MySQL sink changefeed was influenced by the Kafka sink changefeed when network isolation was introduced between CDC and Kafka:

After this PR, only Kafka sink changefeed lag increasing during network isolation injection:

Questions

Will it cause performance regression or break compatibility?

Do you need to update user documentation, design documentation or monitoring documentation?

Release note

Fix a bug that causes the processor tick to get stuck when the downstream is Kafka and becomes unreachable.```

[ti-chi-bot]

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[ti-chi-bot]

This cherry pick PR is for a release branch and has not yet been approved by triage owners.
Adding the do-not-merge/cherry-pick-not-approved label.

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[ti-chi-bot]

@ti-chi-bot: The following tests failed, say /retest to rerun all failed tests or /retest-required to rerun all mandatory failed tests:

Test name	Commit	Details	Required	Rerun command
jenkins-ticdc/verify	a56e151	link	true	/test verify
pull-dm-integration-test	a56e151	link	true	/test dm-integration-test
pull-cdc-integration-storage-test	a56e151	link	true	/test cdc-integration-storage-test
pull-cdc-integration-kafka-test	a56e151	link	true	/test cdc-integration-kafka-test
pull-cdc-integration-mysql-test	a56e151	link	true	/test cdc-integration-mysql-test
pull-dm-compatibility-test	a56e151	link	true	/test dm-compatibility-test

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