### 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)

ARG_IGNORE_DEPENDS_ON_PAST = Arg(
    ("-I", "--ignore-depends-on-past"),
    help="Deprecated -- use `--depends-on-past ignore` instead. "
    "Ignore depends_on_past dependencies (but respect upstream dependencies)",
    action="store_true",
)
ARG_DEPENDS_ON_PAST = Arg(
    ("-d", "--depends-on-past"),
    help="Determine how Airflow should deal with past dependencies. The default action is `check`, Airflow "
    "will check if the the past dependencies are met for the tasks having `depends_on_past=True` before run "
    "them, if `ignore` is provided, the past dependencies will be ignored, if `wait` is provided and "
    "`depends_on_past=True`, Airflow will wait the past dependencies until they are met before running or "
    "skipping the task",
    choices={"check", "ignore", "wait"},
    default="check",
)
ARG_SHIP_DAG = Arg(
    ("--ship-dag",), help="Pickles (serializes) the DAG and ships it to the worker", action="store_true"
)
ARG_PICKLE = Arg(("-p", "--pickle"), help="Serialized pickle object of the entire dag (used internally)")
ARG_JOB_ID = Arg(("-j", "--job-id"), help=argparse.SUPPRESS)
ARG_CFG_PATH = Arg(("--cfg-path",), help="Path to config file to use instead of airflow.cfg")
ARG_MAP_INDEX = Arg(("--map-index",), type=int, default=-1, help="Mapped task index")
ARG_MIGRATION_TIMEOUT = Arg(
    ("-t", "--migration-wait-timeout"),
    help="timeout to wait for db to migrate ",
    type=int,
    default=60,
)
ARG_DB_RESERIALIZE_DAGS = Arg(