### Description


We need to access the time at which a given DAG was parsed last.

Airflow Version : 2.2.2 and above.

### Use case/motivation

End users want to run a given DAG post applying the changes they have done on them. This would mean that the DAG should be parsed post the edits done to it. Right now the last parsed time is available by accessing the airflow database only. Querying the database directly is not the best solution to the problem. Ideally airflow should be exposing APIs that end users can consume that can help provide the last parsed time for a given DAG.

### Related issues

Not Aware.

### Are you willing to submit a 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)

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ARG_UPSTREAM = Arg(("-u", "--upstream"), help="Include upstream tasks", action="store_true")
ARG_ONLY_FAILED = Arg(("-f", "--only-failed"), help="Only failed jobs", action="store_true")
ARG_ONLY_RUNNING = Arg(("-r", "--only-running"), help="Only running jobs", action="store_true")
ARG_DOWNSTREAM = Arg(("-d", "--downstream"), help="Include downstream tasks", action="store_true")
ARG_EXCLUDE_SUBDAGS = Arg(("-x", "--exclude-subdags"), help="Exclude subdags", action="store_true")
ARG_EXCLUDE_PARENTDAG = Arg(
    ("-X", "--exclude-parentdag"),
    help="Exclude ParentDAGS if the task cleared is a part of a SubDAG",
    action="store_true",
)
ARG_DAG_REGEX = Arg(
    ("-R", "--dag-regex"), help="Search dag_id as regex instead of exact string", action="store_true"
)
ARG_SAVE = Arg(("-s", "--save"), help="Saves the result to the indicated file.")
ARG_IMGCAT = Arg(("--imgcat",), help="Displays graph using the imgcat tool.", action="store_true")
ARG_RUN_ID = Arg(("-r", "--run-id"), help="Helps to identify this run")
ARG_CONF = Arg(("-c", "--conf"), help="JSON string that gets pickled into the DagRun's conf attribute")
ARG_EXEC_DATE = Arg(("-e", "--exec-date"), help="The execution date of the DAG", type=parsedate)
ARG_REPLACE_MICRO = Arg(
    ("--no-replace-microseconds",),
    help="whether microseconds should be zeroed",
    dest="replace_microseconds",
    action="store_false",
    default=True,
)
ARG_DB_TABLES = Arg(
    ("-t", "--tables"),
    help=lazy_object_proxy.Proxy(
        lambda: f"Table names to perform maintenance on (use comma-separated list).\n"