Go SDK should support reconnect and auto login configuration

### Description

Related to #2964

Currently, Go SDK support request timeout via `context.Context`, but it doesn't support reconnect and auto-login. The connection would be dead after context.Cancel/context.Timeout/io error. User have to manually call Connect() and Login() to reestablish their session.

We need to implement the auto login/reconnect logic for Go SDK.

### Affected area / component

Go SDK

### Proposed solution

_No response_

### Alternatives considered

_No response_

### Contribution

- [x] I'm willing to submit a pull request to implement this feature

### Good first issue

- [ ] I think this could be a good first issue for a new contributor

The issue names the Go SDK and its Connect() and Login() entry points; start by tracing how context cancellation, timeouts, and I/O errors terminate the connection. Define the reconnect and auto-login behavior around those paths, then verify that sessions recover without requiring callers to invoke Connect() and Login() manually.

Written by the indexing model from the issue text.