[Feature] Use paimon cache instead of caffeine2

### Search before asking

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

### Motivation

Introduce cache type for paimon cache and use it instead of caffeine2 cache in `LookupLevels`, `CachingCatalog` and etc.

### Solution

_No response_

### Anything else?

_No response_

### Are you willing to submit a PR?

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

Start by locating the cache implementations and usages in LookupLevels and CachingCatalog, then trace how the existing caffeine2 cache is configured and consumed. Done means introducing a Paimon cache type and replacing the relevant caffeine2 usage across these components and related areas, with behavior preserved.

Written by the indexing model from the issue text.