Identify as exxperts during MCP OAuth

When authenticating with a remote MCP server, exxperts currently registers itself as "Pi Coding Agent". This name can appear on the provider's authorization screen.

The value comes from the default OAuth client metadata in `pi-mcp-adapter`. exxperts already rebrands the adapter's callback pages and UI text in `scripts/patch-mcp-adapter.mjs`, but the external metadata still uses Pi's name and repository URL.

Could exxperts send its own identity by default?

- `client_name`: `exxperts`
- `client_uri`: `https://github.com/EXXETA/exxperts`

Pi attribution belongs in the documentation and NOTICE file. The OAuth client connecting to an external service is exxperts.

Start with scripts/patch-mcp-adapter.mjs and trace how pi-mcp-adapter’s default OAuth client metadata is patched. The work is complete when remote MCP authorization identifies the client as exxperts with its GitHub repository URL, while the existing callback-page and UI rebranding remains intact.

Written by the indexing model from the issue text.