[FEATURE] Native "Save to external storage" (Google Drive, etc.) from Claude Design exports

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

Claude Design can produce deliverables like .pptx slide decks, but the only way out of the studio is a manual browser download. For teams whose canonical storage is Google Drive (or SharePoint, Box, etc.), every export becomes a two-step manual chore: export the .pptx, then re-upload it to the org's Drive — repeated for every iteration of every deck.
There's a one-way asymmetry similar to the one described in #60327, but on the output side: Design can read a team's files to build the design system, but has no path to write a finished artifact back into the team's actual storage system. The artifact lands in a personal Downloads folder, disconnected from where the team expects it to live.
This is awkward because the first-party Claude.ai Google Drive connector already exposes a file-create capability (see #51040, which notes create is supported even though move/rename/delete are not). The missing piece is wiring Design's export action through that connector — or any pluggable storage target — rather than terminating at a browser download.

Proposed Solution

Add a "Save to…" option alongside the existing export/download in Claude Design that targets connected storage backends:

• Google Drive (via the already-connected first-party connector's create-file capability)
• Extensible to other connectors (Box, OneDrive/SharePoint) as they gain write support
• Let the user pick a destination folder, with the export format (.pptx/.pdf/etc.) preserved

Alternative Solutions

Google Drive for Desktop with the browser's download location pointed at the synced folder collapses export+upload into a single export click — but it's per-machine setup and doesn't help with folder targeting or shared drives.
Related issues

• #60327 — Design → Claude Code sync (input-side asymmetry; this FR is the output-side counterpart)
• #51040 — Claude.ai Drive/Gmail/Calendar connectors lack write ops beyond create
• #38467 — Drive connector doesn't surface Office files (relevant: an exported .pptx wouldn't be findable afterward)
• #52292 — Design share URLs unfetchable by unauthenticated clients

Priority

Medium - Would be very helpful

Feature Category

MCP server integration

Use Case Example

Our team's canonical storage is a shared Google Drive. I use Claude Design to build slide decks.

1. I build a slide deck in Claude Design and iterate on it until it's ready to share.
2. I click export to get a .pptx.
3. The file lands in my browser's local Downloads folder — disconnected from where my team actually expects deliverables to live.
4. I open Google Drive in a separate tab, navigate to the right team folder, and manually upload the .pptx.
5. I iterate on the deck again in Design (decks go through several revisions), and repeat steps 2–4 for every single revision.

What I want instead: a "Save to…" option next to export that targets my connected Google Drive, lets me pick the destination folder, and writes the .pptx straight there — collapsing the export-then-manually-reupload loop into one action. This would matter most for teams where Drive (or SharePoint/Box) is the system of record and every Design artifact has to end up there anyway.

Additional Context

_No response_