LogTemplate table not seeded in custom schema causes TypeError when triggering DAG

### Apache Airflow version

Other Airflow 2 version (please specify below)

### If "Other Airflow 2 version" selected, which one?

2.10.4

### What happened?

What happened:
When using a custom schema for the Airflow metadata database, the log_template table is not automatically seeded with default data. As a result, when triggering a DAG, Airflow attempts to set the log_template_id using the following code:

run.log_template_id = int(session.scalar(select(func.max(LogTemplate.__table__.c.id))))
Because the custom schema’s log_template table is empty, the query returns None, and attempting to convert None to an integer raises a TypeError:
TypeError: int() argument must be a string, a bytes-like object or a real number, not 'NoneType'
In contrast, when using the default public schema, the table is seeded with default data, and this error does not occur.

### What you think should happen instead?

The log_template table should be seeded with default data even when using a custom schema—just as it is for the public schema. Alternatively, the code should handle an empty log_template table gracefully (for example, by defaulting to 0 when no rows exist).

### How to reproduce

Create a custom schema in your Airflow metadata database (e.g., my_custom_schema).
Update the Airflow configuration (in airflow.cfg or via the environment variable **sql_alchemy_schema = ${SQL_ALCHEMY_SCHEMA}**
to use your custom schema.

- Start Airflow.
- Run db migrate ( this will add permisssions and tables inside the schema)
- Trigger a DAG via the UI or API.
- Observe that the DAG trigger fails with the following error:
- TypeError: int() argument must be a string, a bytes-like object or a real number, not 'NoneType'
because the log_template table in the custom schema is empty.


### Operating System

docker container- aws ecs

### Versions of Apache Airflow Providers

2.10.4 ( docker image)

### Deployment

Other Docker-based deployment

### Deployment details

we used the offciail docker image from airflow and on top of that we run few commands and deploy it in aws ecs service

### Anything else?

_No response_

### Are you willing to submit 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)

Start with the `db migrate` entry point and inspect how the `log_template` table is seeded for the public and custom schemas. Reproduce the failure by triggering a DAG after migration, then verify that the custom-schema table contains default data or that an empty table is handled without the TypeError.

Written by the indexing model from the issue text.