[Bug] query the dead-letter queue information in Pulsar Manager, the broker's GC grows rapidly

### Search before asking

- [X] I searched in the [issues](https://github.com/apache/pulsar/issues) and found nothing similar.

### Read release policy

- [X] I understand that unsupported versions don't get bug fixes. I will attempt to reproduce the issue on a supported version of Pulsar client and Pulsar broker.

### Version

3.0.1

### Minimal reproduce step

When I query the dead-letter queue information in Pulsar Manager, the broker's GC grows rapidly. The same happens when I use admin commands.

### What did you expect to see?

The broker GC pause does not show significant fluctuations.

### What did you see instead?

When I query the dead-letter queue information in Pulsar Manager, the broker's GC grows rapidly. The same happens when I use admin commands.

### Anything else?

_No response_

### Are you willing to submit a PR?

- [ ] I'm willing to submit a PR!

Start by reproducing the dead-letter queue information query in Pulsar Manager and through the admin commands on Pulsar 3.0.1 while observing broker GC behavior. Trace the broker path serving this information and identify why repeated queries increase GC activity; done means the cause is isolated and the behavior is validated without significant GC fluctuations.

Written by the indexing model from the issue text.