Keep agent profile settings valid across providers (#3331)

* fix(app): keep profile modes scoped to providers

Applying a profile through sequential field setters allowed a provider change
to race mode persistence, poisoning modeless provider preferences with another
provider's mode. Apply profiles as one form transition and heal invalid
provider-scoped mode preferences when profiles are used.

* test(app): cover profile features across providers

packages/app/src/agent-profiles/index.ts

@@ -14,6 +14,7 @@
  * here.
  */
 export type { AgentProfile } from "@getpaseo/protocol/messages";
+export type { MaterializedAgentProfile } from "./internal/materialize-profile";
 export { useAgentProfiles } from "./internal/use-agent-profiles";
 export {
   useAgentProfilePicker,