[Feature]: Injectable WebSocket client factory for RemoteConversation

Is there an existing feature request for this?

• I have searched existing issues and feature requests, and this is not a duplicate.

Problem or Use Case

RemoteConversation constructs WebSocketCallbackClient directly at a single
point in __init__. There is no supported way for a caller to supply a
transport-specific callback client.

The concrete use case is running the controller with --network none, talking to
an agent server over a Unix-domain socket via a relay, so a WebSocket-over-UDS
client is needed in place of the default TCP one.

Today the only way to achieve this is to replace the module global
openhands.sdk.conversation.impl.remote_conversation.WebSocketCallbackClient,
which is process-wide. That prevents two conversations in the same process from
using different transports, and it depends on a private module attribute that is
not part of the public API.

Desired Behavior

Add an optional, keyword-only websocket_client_factory argument to
RemoteConversation, plus a typed WebSocketClientFactory protocol describing
the construction contract (host, conversation_id, callback, api_key,
on_reconnect).

When the argument is omitted, behavior is unchanged: the default
WebSocketCallbackClient is used. The existing client keeps ownership of
startup, readiness waiting, initial reconciliation, failure cleanup, and
shutdown — the factory only decides which client is constructed.

A Protocol is preferred over a bare Callable[..., Any] so an incompatible
factory is rejected at type-check time rather than at WebSocket-connect time.

The default must stay late-bound (resolved when __init__ runs, not captured as
a default argument value), because the existing test suite patches the module
attribute in 87 patch() sites across 10 test files.

Acceptance Criteria

• RemoteConversation accepts an optional websocket_client_factory keyword argument
• A WebSocketClientFactory protocol types the contract with host, conversation_id, callback, api_key, and on_reconnect
• An injected factory is used instead of the default, and receives all five keyword arguments
• Omitting the argument still constructs WebSocketCallbackClient, resolved at call time so existing module-level patching keeps working
• WebSocketCallbackClient satisfies the protocol's keyword contract
• uv run pytest tests/sdk/conversation passes with no new failures

Alternatives Considered

Replacing the module global WebSocketCallbackClient at runtime. This works, but
it is process-wide, so conversations cannot use independent transports, and it
relies on a private attribute with no compatibility guarantee.

Subclassing RemoteConversation to override client construction. The
construction is inline in __init__ rather than in an overridable method, so
this would mean copying the whole __init__ body.

Priority / Severity

Medium - Would improve experience

Estimated Scope

Small - API addition, config option, or minor change

Feature Area

• Agent API / Core functionality
• Tools / Tool system
• Skills / Plugins
• Agent Server
• Workspace management
• Configuration / Settings
• Examples / Templates
• Documentation
• Testing / Development tools
• Performance / Optimization
• Integrations (GitHub, APIs, etc.)
• Other

Technical Implementation Ideas (Optional)

No response

Additional Context

No response

Start in openhands.sdk.conversation.impl.remote_conversation, focusing on RemoteConversation.init and the existing WebSocketCallbackClient construction. Read the tests under tests/sdk/conversation, then run uv run pytest tests/sdk/conversation while checking the acceptance criteria: the injected factory receives all five keyword arguments, and the default remains late-bound and compatible with existing patches.