refactor: extract skill save context, stabilize mutation dependency, and deduplicate cache updates

Split SkillSaveContext and useSkillSaveManager into a separate file to
fix react-refresh/only-export-components lint error. Destructure
mutateAsync from useUpdateAppAssetFileContent for a stable callback
reference, preventing unnecessary useCallback cascade rebuilds. Extract
shared patchFileContentCache helper to unify setQueryData logic between
updateCachedContent and the collaboration event handler.

web/app/components/workflow/skill/hooks/skill-save-context.ts

@@ -0,0 +1,19 @@
+import type { FallbackEntry, SaveFileOptions, SaveResult } from './use-skill-save-manager'
+import * as React from 'react'
+
+type SkillSaveContextValue = {
+  saveFile: (fileId: string, options?: SaveFileOptions) => Promise<SaveResult>
+  saveAllDirty: () => void
+  registerFallback: (fileId: string, entry: FallbackEntry) => void
+  unregisterFallback: (fileId: string) => void
+}
+
+export const SkillSaveContext = React.createContext<SkillSaveContextValue | null>(null)
+
+export const useSkillSaveManager = () => {
+  const context = React.useContext(SkillSaveContext)
+  if (!context)
+    throw new Error('Missing SkillSaveProvider in the tree')
+
+  return context
+}