[kv snapshot lease] Reduce the external IO operation when send source event to coordinator when FlinkSourceReader do snapshot state

### Search before asking

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

### Motivation

Reduce the external IO operation when send source event to coordinator when FlinkSourceReader do snapshot state. See comment: https://github.com/apache/fluss/pull/2179#discussion_r2777638637

### Solution

_No response_

### Anything else?

_No response_

### Willingness to contribute

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

Start by reading FlinkSourceReader's snapshot state flow and the discussion linked from PR 2179. Trace how source events are sent to the coordinator and identify the external IO that can be avoided. Done means the snapshot path performs fewer external IO operations without changing coordinator behavior.

Written by the indexing model from the issue text.