Extract client SDK package (#1052)

* Extract client SDK package

* Polish SDK client identity defaults

* Build client before dependent CI jobs

* Restore daemon client server export

* Extract protocol and client SDK packages

* Fix provider override schema validation

* Fix app test daemon client imports

* Simplify workspace build targets

* Fix CLI test server build bootstrap

* Run SDK package tests in CI

* Fix rebase package split drift

* Restore lockfile registry metadata

* Update SDK config test for prompt default

* Move terminal stream router test to client package

* Fix rebase drift for protocol imports

* Fix SDK agent capability fixture

* Restore legacy server client exports

* Fix server export compatibility test

* Advertise custom mode icon client capability

* Remove server daemon-client exports

* Format rebased mode control import

* Fix rebase drift for protocol imports

Files added by upstream PRs (#893, #1147, #1154) referenced the pre-split
shared/ paths that this branch moves into @getpaseo/protocol. Redirect
those imports to the protocol package so typecheck stays green after the
rebase.

packages/server/CLAUDE.md

@@ -14,7 +14,7 @@ Paseo is a mobile + CLI app for monitoring and controlling local AI coding agent
 
 ```bash
 npm run dev                          # Start daemon + Expo in Tmux
-npm run build:daemon                 # Build: highlight + relay + server + cli
+npm run build:server                 # Build: highlight + relay + protocol + client + server + cli
 npm run typecheck                    # Typecheck all packages
 npm run test                         # Test all packages
 npm run format                       # Format with Biome (in-place)
@@ -49,8 +49,7 @@ npm run test:ui                     # Vitest UI at localhost:51204
 ### Other useful commands
 
 ```bash
-npm run build --workspace=@getpaseo/relay    # Rebuild relay before daemon
-npm run build --workspace=@getpaseo/server   # Rebuild server
+npm run build:server                         # Rebuild server stack
 npm run db:query -- "SELECT ..."             # Run arbitrary SQL
 npm run cli -- ls -a -g                      # List agents
 npm run cli -- daemon status                 # Check daemon status
@@ -168,7 +167,6 @@ packages/server/src/
 │       └── agent-storage.ts  # File-backed JSON persistence
 ├── providers/                 # Claude, Codex, Copilot, OpenCode, Pi adapters
 ├── relay-transport.ts        # Outbound relay connection
-└── client/daemon-client.ts   # Client library for daemon connection
 ```
 
 Agent state persists to `$PASEO_HOME/agents/{cwd-with-dashes}/{agent-id}.json`