Consider swapping `httpx` usage for `httpx2`

### Under which category would you file this issue?

Airflow Core

### Apache Airflow version

3.x

### What happened and how to reproduce it?

At the time of writing, it appears that the `httpx` library might not be actively maintained. There are a number of bug-fixes for `httpx` which have not landed, but which are present in [`httpx2`](https://httpx2.pydantic.dev/) (forked from `httpx==0.28.1`).

Additionally, the maintainer of `starlette` (one of the key sub-dependencies of `FastAPI`) [has confirmed](https://github.com/pydantic/httpx2/discussions/980#discussioncomment-17030187) that starlette will migrate to `httpx2`. So it seems the migration from `httpx` in `FastAPI` is an eventuality.

### What you think should happen instead?

Any direct usage of `httpx` within airflow-core / the task-sdk / airflow's providers should probably migrate to httpx2.

The scope of this change is obviously large; but the migration of direct code reliance on `httpx` is [relatively straightforward](https://httpx2.pydantic.dev/migration/).

I'd imagine it would be good to add individual, well-defined / scoped sub-issues for this.

### Operating System

_No response_

### Deployment

_No response_

### Apache Airflow Provider(s)

_No response_

### Versions of Apache Airflow Providers

_No response_

### Official Helm Chart version

Not Applicable

### Kubernetes Version

_No response_

### Helm Chart configuration

_No response_

### Docker Image customizations

_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)

Start by inventorying direct httpx usage across airflow-core, the task-sdk, and Airflow providers, then read the httpx2 migration guide linked in the issue. The scope is broad, so identify well-defined sub-issues for individual areas. Done means the selected direct usages have migrated to httpx2 and their affected tests or checks pass.

Written by the indexing model from the issue text.