Custom connector to sheetsmcp.googleapis.com fails with "caller does not have permission" on every call (same bug class as #218)

### MCP server URL or name

https://sheetsmcp.googleapis.com/mcp/v1

### How are you connecting to this server?

From a custom connector URL I entered manually

### Where does the issue occur?

During a conversation (after initial auth)

### When did you last reproduce this?

2026-08-16 10:04 am GMT

### Browser and OS

Claude cowork desktop

### Describe the issue

Connector authenticates successfully — claude.ai shows "Connected" — but every tool call made afterward mid-conversation fails with "The caller does not have permission." Reproduced repeatedly, most recently 2026-08-16 via get_spreadsheet on a spreadsheet the authenticated account owns and has edit access to.

Ruled out before concluding this is a platform bug (same class as #218):
- Account mismatch: confirmed the Google account used for the OAuth grant, the GCP console project, and the target file's owner are all the same account.
- Missing scopes: Google's own setup guide for this MCP server requires drive.readonly, drive.file, spreadsheets.readonly, spreadsheets. Initially only 3 of 4 were configured; added the missing .readonly scope so all were present and visible on the consent screen during authorization.
- Stale/cached token: fully revoked access server-side via myaccount.google.com/permissions → app → "Delete all" (not just claude.ai's Disconnect button), then reconnected from scratch with a brand-new consent screen showing all scopes.

Error was identical before and after all of the above. A separate, older custom connector to Google's Drive MCP server, authorized under the same account, works correctly on the same files — so this is specific to the Sheets MCP endpoint, not a general OAuth problem. Steps to reproduce: create a GCP project, enable sheets.googleapis.com and sheetsmcp.googleapis.com, configure OAuth consent with the 4 scopes above, add https://sheetsmcp.googleapis.com/mcp/v1 as a custom connector, complete auth, then call get_spreadsheet or get_values on any owned file.

Related: #218 (Google People API, same error message and root cause theory) and #42 (referenced in #218 as an earlier instance of the same scope-forwarding bug class).

### Error details

```shell
The caller does not have permission

No pop-up error or error ID was shown in the claude.ai UI — this is the raw error text returned by the tool call itself when the connector is used (e.g. via get_spreadsheet).
```

### Expected behavior

Tool call succeeds and returns the spreadsheet's content/metadata, matching the access already granted on the OAuth consent screen.

### Additional context

Impact: Google's official Sheets remote MCP server is currently unusable from claude.ai via custom connector, blocking any workflow that needs Claude to read or edit live Google Sheets content directly. A companion issue for the Docs MCP endpoint (docsmcp.googleapis.com), which fails identically, is being filed separately per the "one issue per server" guidance on this form.