[Chat] Send the MCP server's Warp-side identity in MCPContext

[Legoben]

Description

The installation id the client reports in MCPContext.servers[].id (and that comes back as CallMCPTool.server_id) is, for cloud runs, UUIDv5(task_id, spec_token, server_name). The spec token is the run config's warp_id — a managed MCP server uid or a well-known integration id such as linear — and it was hashed into the id and then discarded, so nothing downstream (warp-server, the Factory run transcript) could name the server behind an MCP call.

This keeps it and sends it alongside the opaque id:

• TemplatableMCPServerInstallation gains warp_id: Option<String> (#[serde(default)], with_warp_id, warp_id()); installations_from_managed_client_config_json records the spec token.
• TemplatableMCPServerInfo carries it through runtime::spawn_server (new parameter; the one native caller passes installation.warp_id()).
• MCPServer.warp_id in the request model. convert_to.rs turns it into MCPContext.MCPServer.identity, an MCPServerIdentity: integration (the new MCPIntegration enum — LINEAR, SLACK, JIRA, LINEAR_AGENT_SESSION, mirroring warp-server's well-known id registry) for a well-known id, managed_server_uid for a uuid, and no identity at all for an empty id or one this build does not know, so a newer server-side integration is unnamed rather than misattributed. display_name is left unset; MCPContext.MCPServer.name already carries it and warp-server fills it in when it copies the identity onto tool calls.

Local and ad-hoc servers send no identity. Nothing about the installation id itself changes: it stays the key the manager and permissions use, and the identity travels as a separate field.

Stacked on #15947 (bens/populate-user-query-attribution), which already adapts this repo to the attribution protos. warp_multi_agent_api moves from that branch's c8ed32b to b430a4f: warp-proto-apis branch bens/populate-user-query-attribution-plus-mcp-identity, which is #381's head merged with main at the MCPServerIdentity change (#380), so both sets of fields are in one tree. Once #381 merges, that rev collapses to a main sha.

Downstream: warp-server #17255 copies the identity onto each MCP tool call as server_identity, filling display_name from name; warp-server #17260 renders it.

Linked Issue

No GitHub issue; spec is warp-server specs/factory-threads-viewer/TECH.md (A4 / C8).

• The linked issue is labeled ready-to-spec or ready-to-implement.
• Where appropriate, screenshots or a short video of the implementation are included below.

Testing

Against a local proto checkout carrying the new fields ([patch] not included in this PR):

• cargo check -p mcp and cargo check -p warp --lib --tests clean; cargo fmt --check clean.

• New tests: mcp_startup::tests::managed_config_installations_carry_the_spec_token_as_warp_id (well-known slug and managed uid both survive as warp_id) and convert_to::tests::mcp_context_servers_carry_their_identity_alongside_the_installation_id (well-known id → integration; uuid → managed_server_uid; display name left to name; empty and unknown ids → no identity).

• Not manually run end to end: needs a cloud run with a well-known integration to observe mcp_context.servers[].identity.integration == LINEAR in the request.

• I have manually tested my changes locally with ./script/run

Agent Mode

• Warp Agent Mode - This PR was created via Warp's AI Agent Mode

CHANGELOG-NONE