refactor(gateway): use withContext for coroutines instead of duplicating files

Address PR #6098 review feedback to avoid copying entire Gateway files
for IDE version compatibility.

Changes:
- Replace deprecated coroutine APIs with withContext(getCoroutineBgContext())
  - startChildSyncIOBackgroundAsync().await() → withContext
  - lifetime.launchIOBackground → withContext
  - lifetime.launchOnUiAnyModality → lifetime.launchOnUi
  - launchChildSyncIOBackground → withContext
- Remove manual CoroutineScope + SupervisorJob creation
- Move files to common src/ directory (works across all IDE versions)
- Delete duplicated src-242-252/ and src-253+/ versions

The withContext API is available in all IDE versions, eliminating the need
for version-specific file duplication. Coroutine scopes now properly inherit
from parent contexts instead of manually creating SupervisorJobs.

Tested:
- ✅ Compiles for IDE 2024.2-2025.2
- ✅ Compiles for IDE 2025.3+
- ✅ Detekt code style checks pass

Author: aseemxs