AsyncSchemaRegistryClient is unable to handle concurrent requests

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**Describe the bug**

Related to https://github.com/encode/httpx/issues/1478, I'm getting this exception while using the same instance of `AsyncSchemaRegistryClient` in two different places, raising `httpx.RemoteProtocolError: can't handle event type ConnectionClosed when role=SERVER and state=SEND_RESPONSE`. The source code of the client is similar to the [example that shows how to reproduce the issue in httpx](https://github.com/encode/httpx/issues/1478#issuecomment-828955977) and the [answer to this comment](https://github.com/encode/httpx/issues/1478#issuecomment-829132394) mentions using the context manager once at a time would be the fix to it.

I could manage to overcome this issue by creating one instance of the client for every class that depends on `AsyncSchemaRegistryClient`

**To Reproduce**
Steps to reproduce the behavior:

I'll need some time to write a small snippet to reproduce it, so bear with me 😬

**Expected behavior**

The client is able to handle two (or more) concurrent calls to the schema registry

Start at the AsyncSchemaRegistryClient entry point and review how its shared client or context manager is used during concurrent calls. Use the linked HTTPX reproduction and discussion as context, then create a concurrent reproduction before changing behavior. Done means one shared client can handle two or more concurrent schema-registry calls without the reported RemoteProtocolError.

Written by the indexing model from the issue text.