Unify MIT partial merging strategy with other partial update modes

### Task Description

**What needs to be done:**

This is a followup ticket. That we want to unify partial merging for MIT and other partial update modes, like ignore_default.

**Why this task is needed:**
Improve code readability, easier for maintenance.

### Task Type

Code improvement/refactoring

### Related Issues

**Parent feature issue:** (if applicable )
https://issues.apache.org/jira/browse/HUDI-8401
**Related issues:**
PR comment related: https://github.com/apache/hudi/pull/13615/#discussion_r2274253729
Initial PR: https://github.com/apache/hudi/pull/13623
NOTE: Use `Relationships` button to add parent/blocking issues after issue is created.

The issue names no files or tests; start by reviewing the parent HUDI-8401 issue, the initial PR #13623, and the referenced discussion in PR #13615. Compare how MIT and ignore_default partial update modes currently merge, then verify that their strategies are unified without changing the intended update behavior.

Written by the indexing model from the issue text.