Remove postgres subcharts from Airflow Helm Charts

### Body

Bitnami (now VMware) has restricted access to newer postgres images in their main repository. This affects all KinD-based testing and development workflows, as temporary workaround we have used `docker.io/postgres` images: https://github.com/apache/airflow/pull/55820 but over a long term, we should remove that subchart as discussed in lazy consensus too: https://lists.apache.org/thread/3o4wj76pmd2m13jho7sxcbfkbgpv88h9

The plan of action could be:

* Remove postgres dependency entirely from the helm chart (lazy consensus has been achieved: https://lists.apache.org/thread/3o4wj76pmd2m13jho7sxcbfkbgpv88h9)
* Make sqlite the default database in values.yaml for development/testing
* Update CI/CD pipelines to use sqlite
* Eliminate bitnami dependency
* Users can extend our helm charts and provide their own DBs on top of it.

### Committer

- [x] I acknowledge that I am a maintainer/committer of the Apache Airflow project.

Start with the Helm chart and values.yaml, then trace the CI/CD pipelines and KinD-based development and testing workflows that consume the PostgreSQL dependency. Confirm all Bitnami references before making changes, and consider the work done when the chart uses SQLite by default, pipelines use SQLite, the Bitnami dependency is gone, and users can provide external databases.

Written by the indexing model from the issue text.