Follow-up: Add broader mutation-path coverage for public-inclusive input cache invalidation

## Context

Identified as a follow-up item in PR #11873.

## Problem

The public-inclusive input asset cache introduced in #11873 (`assetService.getInputAssetsIncludingPublic()`) currently has invalidation coverage for a limited set of mutation paths. As the cache gains more consumers, additional mutation paths may need to trigger invalidation to keep the cache consistent.

## Proposed Work

Once the cache has more consumers, review all mutation paths that can change input assets and ensure each triggers `assetService.invalidateInputAssetsIncludingPublic()`. Add test coverage for any newly identified invalidation paths.

## References

- PR: https://github.com/Comfy-Org/ComfyUI_frontend/pull/11873
- Requested by: @jaeone94

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-11883-Follow-up-Add-broader-mutation-path-coverage-for-public-inclusive-input-cache-invali-3566d73d365081f091cfda0f207ba497) by [Unito](https://www.unito.io)