[MM] MultimodalInputs.merge: adopt the M-RoPE delta and clear its decode cache - #41739

Motivation

MultimodalInputs.merge (session continuation) drops the new turn's M-RoPE position delta when the earlier turn had none, and never clears mrope_position_delta_repeated_cache. Decode positions after a multimodal session continuation then come from a stale or missing delta.

Modifications

• merge() adopts the other input's delta when self has none, and always clears mrope_position_delta_repeated_cache.
• test/registered/unit/managers/test_mm_inputs_merge_mrope_delta.py.

Accuracy Tests

CPU: 1 passed. With the schedule_batch.py change reverted: 1 failed.

Speed Tests and Profiling

No hot-path change beyond the fix itself; not separately benchmarked.

Checklist

• Format your code according to the Format code with pre-commit.
• Add unit tests according to the Run and add unit tests.
• Update documentation according to Write documentations.
• Provide accuracy and speed benchmark results according to Test the accuracy and Benchmark the speed.
• Follow the SGLang code style guidance.

Review and Merge Process

1. Ping Merge Oncalls to start the process. See the PR Merge Process.
2. Get approvals from CODEOWNERS and other reviewers.
3. Trigger CI tests with comments or contact authorized users to do so.
   • Common commands include /tag-and-rerun-ci, /tag-run-ci-label, /rerun-failed-ci
4. After green CI and required approvals, ask Merge Oncalls or people with Write permission to merge the PR.

CI States

Latest PR Test (Base): ✅ Run #36767650274
Latest PR Test (Extra): ❌ Run #36767649664
Latest PR Test (AMD ROCm 10): ❌ Run #36767650253