[SPARK-51266][CORE] Remove the unused definition of `private[spark] o…

…bject TaskDetailsClassNames`

### What changes were proposed in this pull request?
`TaskDetailsClassNames` was no longer used by other code in Spark after the cleanup of the `TaskPagedTable` definition in SPARK-44490, so this PR removes it from the code.

### Why are the changes needed?
Code clenaup.

### Does this PR introduce _any_ user-facing change?
No, `TaskDetailsClassNames` is an internal definition of Apache Spark.

### How was this patch tested?
- Pass GitHub Actions

### Was this patch authored or co-authored using generative AI tooling?
No

Closes #50016 from LuciferYang/remove-TaskDetailsClassNames.

Authored-by: yangjie01 <yangjie01@baidu.com>
Signed-off-by: Dongjoon Hyun <dongjoon@apache.org>