DateTimeSensorAsync crashes Dag parsing with templated target_time + start_from_trigger=True

### Apache Airflow version

main (also reproduced against current released 3.x)

### What happened

`DateTimeSensorAsync` declares `target_time` as a `template_fields` member (rendered via Jinja against the run context at task-execution time), but its `__init__` calls `timezone.parse(self.target_time)` at Dag-parse time when `start_from_trigger=True` — before Jinja rendering has happened. If `target_time` is a template string (the normal, documented use case for this field), this raises a parser error and crashes parsing of the entire Dag
file, not just the task.

This is the same root-cause pattern fixed for `TimeSensor` in #69610 (parse-time handling of a value that can only correctly be resolved at/near task-execution time), but with a more severe symptom: instead of silent `dag_version` churn, the whole Dag fails to parse.

### Reproduction

```python
from __future__ import annotations
import pendulum
from airflow.sdk import DAG
from airflow.providers.standard.sensors.date_time import DateTimeSensorAsync

with DAG(dag_id="repro", schedule=None, start_date=pendulum.datetime(2026, 1, 1, tz="UTC")):
DateTimeSensorAsync(
task_id="t",
target_time="{{ data_interval_end.tomorrow().replace(hour=1) }}",
start_from_trigger=True,
)
```

Raises at Dag-parse time:

```
pendulum.parsing.exceptions.ParserError: Invalid date string: {{ data_interval_end.tomorrow().replace(hour=1) }}
```

There is currently no test coverage for `DateTimeSensorAsync` combining a templated `target_time` with `start_from_trigger=True`.

### What you think should happen instead

Check whether a string is passed when start_from_trigger=True. static datetime should be fine

### How to reproduce

See reproduction script above; raises immediately on Dag parse.

### Operating System

N/A (reproduced via `breeze` container, standard provider)

### Deployment

Other

### Deployment details

Found while reviewing #69610 (`TimeSensor` fix for a related parse-time issue).

### Anything else

Related: #69610, #69543

### 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)

Start at DateTimeSensorAsync in airflow/providers/standard/sensors/date_time.py and run the reproduction DAG with start_from_trigger=True. Add test coverage for static and templated target_time values, verifying that DAG parsing succeeds for the templated case while static datetimes continue to work.

Written by the indexing model from the issue text.