dag_processing.last_duration.<dag_file> metric missing

### Apache Airflow version

Other Airflow 3 version (please specify below)

### If "Other Airflow 3 version" selected, which one?

3.0.6

### What happened?

Prior to version 3x, Airflow emitted the `dag_processing.last_duration.` metric. While working in MWAA with version 3.0.6, I noticed this metric is no longer available in CloudWatch. I verified MWAA is not excluding any metrics, so I expect the metric to be present.

For a sanity check, I enabled StatsD in Breeze to see if the metric is emitted or not. I don't see the metric in Grafana.

The other python file-level metric (dag_processing.last_run.seconds_ago.) is still emitted and visible in CloudWatch.

The metric is still listed in the [Airflow metrics documentation](https://airflow.apache.org/docs/apache-airflow/3.0.6/administration-and-deployment/logging-monitoring/metrics.html#timers).

### What you think should happen instead?

I expected the metric to be present. I find it useful when identifying python files that may need to be tuned for performance.

### How to reproduce

For MWAA, create an MWAA environment with version 3.0.6 and upload a python file (with dag) to the Amazon S3 bucket. Once parsing takes place, attempt to find the metric in Amazon CloudWatch.

### Operating System

AL2023

### Versions of Apache Airflow Providers

_No response_

### Deployment

Amazon (AWS) MWAA

### Deployment details

This is a standard MWAA deployment. I did not add/modify any of the `[metrics]` config items.

### Anything else?

_No response_

### Are you willing to submit PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [x] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

Start with the Airflow metrics documentation and reproduce the issue by enabling StatsD in Breeze, comparing the missing last_duration metric with dag_processing.last_run.seconds_ago. Trace the metric emission path and verify the result in StatsD or Grafana; done means the metric is emitted again and remains consistent with the documented timers.

Written by the indexing model from the issue text.