### What changes were proposed in this pull request?

This PR mainly targets:

1. Expose only explain(mode: String) in Scala side
2. Clean up related codes
    - Hide `ExplainMode` under private `execution` package. No particular reason but just because `ExplainUtils` exists there
    - Use `case object` + `trait` pattern in `ExplainMode` to look after `ParseMode`.
    -  Move `Dataset.toExplainString` to `QueryExecution.explainString` to look after `QueryExecution.simpleString`, and deduplicate the codes at `ExplainCommand`.
    - Use `ExplainMode` in `ExplainCommand` too.
    - Add `explainString` to `PythonSQLUtils` to avoid unexpected test failure of PySpark during refactoring Scala codes side.

### Why are the changes needed?

To minimised exposed APIs, deduplicate, and clean up.

### Does this PR introduce any user-facing change?

`Dataset.explain(mode: ExplainMode)` will be removed (which only exists in master).

### How was this patch tested?

Manually tested and existing tests should cover.

Closes #26898 from HyukjinKwon/SPARK-30200-followup.

Authored-by: HyukjinKwon <gurwls223@apache.org>
Signed-off-by: HyukjinKwon <gurwls223@apache.org>