[BUG] Cowork session has no in-session skill save/update path or confirmation — inconsistent with other sessions

Reported by a user (Aviv) who says this normally works in other sessions: he is usually able to have Claude update or create a skill directly and know it landed. In this session, that capability was not available.

What this session actually had available, checked directly:

• No MCP tool exposed for writing/updating a skill in the user's account. Searched loaded and deferred tools; the only skill-related tools present belonged to unrelated third-party MCP connectors (Alta_MCP's load_skill, monday.com's manage_agent_skills), not a Claude/Cowork skill-write tool.
• /root/.claude/skills/synced/ on disk is a read-only cache of the user's existing skills (confirmed structure: one dir per skill, e.g. browserbase-linkedin-aviv/, plus manifest.json). Editing files there does not propagate back to the account, per the system prompt's explicit note that this cache is read-only.
• The skill-creator skill available in this session is for authoring/optimizing skill content, not for persisting it — it doesn't expose a save/write action either.
• The documented mechanism is: write the skill as a file, call SendUserFile, and hope the client surfaces a save option on the file card. The agent receives no callback, event, or status on whether the user actually saved it. The system prompt is explicit: "You get no signal whether they saved it: report the skill as delivered, never as saved."

This produced a bad user experience: the user asked for an existing skill (browserbase-linkedin-aviv) to be updated with a bug fix, got a file delivered with no explanation of what to do with it, and reasonably read this as the agent not knowing how to do something it should know how to do — because in his other sessions, updating a skill apparently does work with some kind of confirmable outcome.

Since the user reports this working elsewhere, the likely root cause is one of:

1. A save-confirmation UI affordance exists on the file card in some clients/surfaces but was not rendered or reachable in this session's surface.
2. A skill-write tool is normally injected into session tool lists (locally or via MCP) but was missing/not connected for this session.
3. Session/account state (e.g. plugin vs. non-plugin skill, sync timing) put this skill outside whatever write path normally applies.

Requesting investigation into why this session lacked whatever mechanism normally lets skill updates be confirmed, and a consistent, discoverable path (tool-mediated write with a real result, or a documented and reliably-rendered save UI) so this doesn't present as agent incompetence when it's actually a platform/session gap.