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/app/vitest.config.ts

@@ -84,7 +84,6 @@ export default defineConfig({
         replacement: path.resolve(__dirname, "../relay/src/index.ts"),
       },
       { find: "@", replacement: path.resolve(__dirname, "src") },
-      { find: "@server", replacement: path.resolve(__dirname, "../server/src") },
       // Point to the ESM build so Vite can transform its imports and apply the
       // react alias below (the CJS build uses require('react') which bypasses
       // Vite alias resolution).