### Apache Airflow version

2.4.1

### What happened

When there are large number of dag files, lets say 10K and each takes sometime to parse,  dag_parser doesnt pick any newly created files till all 10k files are finished parsing

`if not self._file_path_queue:
                self.emit_metrics()
                self.prepare_file_path_queue()`

Above logic only adds new files to queue when queue is empty

### What you think should happen instead

Every loop of dag processor should pick new files and add into file for parsing queue

### How to reproduce

_No response_

### Operating System

All

### Versions of Apache Airflow Providers

_No response_

### Deployment

Docker-Compose

### Deployment details

_No response_

### Anything else

_No response_

### Are you willing to submit PR?

- [X] 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)

pickle_dags=False,
            async_mode=True,
        )
        manager._run_parsing_loop()
        result = None
        while parent_pipe.poll(timeout=None):
            result = parent_pipe.recv()
            if isinstance(result, DagParsingStat) and result.done:
                break
        
        assert sum(stat.run_count for stat in manager._file_stats.values()) == 3
        with create_session() as session:
            assert session.query(DagModel).get(dag_id) is not None
    @conf_vars({("core", "load_examples"): "False"})
    @pytest.mark.backend("mysql", "postgres")
    @pytest.mark.execution_timeout(30)
    @mock.patch("airflow.dag_processing.manager.DagFileProcessorProcess")
    def test_pipe_full_deadlock(self, mock_processor):
        dag_filepath = TEST_DAG_FOLDER / "test_scheduler_dags.py"
        child_pipe, parent_pipe = multiprocessing.Pipe()
        
        for fd in (parent_pipe.fileno(),):
            sock = socket.socket(fileno=fd)
            sock.setsockopt(socket.SOL_SOCKET, socket.SO_SNDBUF, 1024)
            sock.setsockopt(socket.SOL_SOCKET, socket.SO_RCVBUF, 1024)
            sock.detach()
        exit_event = threading.Event()
        
        
        def keep_pipe_full(pipe, exit_event):