refactor: broader function decomposition for cognitive complexity in missing-model pipeline

## Follow-up from PR #11751

**Context:**
PR #11751 (https://github.com/Comfy-Org/ComfyUI_frontend/pull/11751) extracted the missing-model pipeline orchestration from `ComfyApp` into `src/platform/missingModel/missingModelPipeline.ts`. This was intentionally refactor-heavy and deferred some improvements.

**Task:**
Perform broader function decomposition within the missing-model pipeline to reduce cognitive complexity. Break down large functions into smaller, focused units to improve readability and maintainability.

**Relevant files:**
- `src/platform/missingModel/missingModelPipeline.ts`

**Requested by:** @jaeone94 in https://github.com/Comfy-Org/ComfyUI_frontend/pull/11751

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