[Feature] Refactor the ability of full-compaction into TableWrite

### Search before asking

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

### Motivation

Note: This work is difficult, please participate carefully.

We can refactor the ability of full-compaction into StreamTableWrite & BatchTableWrite, in this way, every engines can work with full-compaction.

### Solution

_No response_

### Anything else?

_No response_

### Are you willing to submit a PR?

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

Start by locating StreamTableWrite and BatchTableWrite, then trace where full-compaction is currently implemented and how the streaming and batch engines invoke table writes. Done means full-compaction is available through both writers so every engine can use it.

Written by the indexing model from the issue text.