Pulsar Pub Sub - Providing Persistent Connections over Websockets while Publishing from the Browser

### Search before asking

- [x] I searched in the [issues](https://github.com/apache/pulsar/issues) and found nothing similar.

### Motivation

I have limited number of web clients. While subscription to a topic remains persistent, publishing to a topic is not persistent. I need to open and close connections each time I have to send data.

I am building a enterprise Fintech Application. Could you kindly provide this feature for native websocket based communication that pulsar supports ?

### Solution

_No response_

### Alternatives

_No response_

### Anything else?

_No response_

### Are you willing to submit a PR?

- [ ] I'm willing to submit a PR!

Start by tracing Pulsar’s native WebSocket publishing path and comparing it with the persistent subscription behavior described in the issue. Determine the API and connection-lifecycle changes needed for persistent browser publishing, then define tests that verify a connection can publish multiple messages without reopening it.

Written by the indexing model from the issue text.