### 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)

default=conf.get("celery", "FLOWER_BASIC_AUTH"),
    help=(
        "Securing Flower with Basic Authentication. "
        "Accepts user:password pairs separated by a comma. "
        "Example: flower_basic_auth = user1:password1,user2:password2"
    ),
)
ARG_TASK_PARAMS = Arg(("-t", "--task-params"), help="Sends a JSON params dict to the task")
ARG_POST_MORTEM = Arg(
    ("-m", "--post-mortem"), action="store_true", help="Open debugger on uncaught exception"
)
ARG_ENV_VARS = Arg(
    ("--env-vars",),
    help="Set env var in both parsing time and runtime for each of entry supplied in a JSON dict",
    type=json.loads,
)
ARG_CONN_ID = Arg(("conn_id",), help="Connection id, required to get/add/delete/test a connection", type=str)
ARG_CONN_ID_FILTER = Arg(
    ("--conn-id",), help="If passed, only items with the specified connection ID will be displayed", type=str
)
ARG_CONN_URI = Arg(
    ("--conn-uri",), help="Connection URI, required to add a connection without conn_type", type=str
)
ARG_CONN_JSON = Arg(
    ("--conn-json",), help="Connection JSON, required to add a connection using JSON representation", type=str
)
ARG_CONN_TYPE = Arg(
    ("--conn-type",), help="Connection type, required to add a connection without conn_uri", type=str
)
ARG_CONN_DESCRIPTION = Arg(