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/package.json

@@ -63,7 +63,9 @@
   "dependencies": {
     "@agentclientprotocol/sdk": "^0.17.1",
     "@anthropic-ai/claude-agent-sdk": "^0.2.133",
+    "@getpaseo/client": "0.1.83",
     "@getpaseo/highlight": "0.1.83",
+    "@getpaseo/protocol": "0.1.83",
     "@getpaseo/relay": "0.1.83",
     "@isaacs/ttlcache": "^2.1.4",
     "@modelcontextprotocol/sdk": "^1.20.1",