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/src/utils/worktree.ts

@@ -16,8 +16,8 @@ export {
   PaseoConfigSchema,
   type PaseoConfig,
   type PaseoConfigRaw,
-} from "./paseo-config-schema.js";
-import { PaseoConfigSchema, type PaseoConfig } from "./paseo-config-schema.js";
+} from "@getpaseo/protocol/paseo-config-schema";
+import { PaseoConfigSchema, type PaseoConfig } from "@getpaseo/protocol/paseo-config-schema";
 import {
   normalizeBaseRefName,
   readPaseoWorktreeMetadata,