Desktop @-mention picker does not list a renamed managed agent (messages render; mobile picker works)

## Summary
After a managed agent was renamed by its owner, another user's **desktop** app no longer offers the agent in the @-mention picker, even though the same channel renders the agent's messages fine and the same user's **mobile** app lists and mentions the agent without issues. App restart on desktop does not help.

## Setup
- Owner machine (macOS, Buzz Desktop): managed agent renamed from `Dory` to `Dory (web admin)` via the agent settings UI on 2026-08-07 ~13:35 UTC. Access set to respond-to-anyone. Agent restarted; verified live.
- Relay state verified correct via CLI from a separate account:
- `buzz users get` returns the new display_name `Dory (web admin)` (kind-0 republished)
- `buzz users presence` shows online
- agent is a member of the channel and **answers non-owner mentions** (tested live)
- CLI-side name resolution of `@Dory (web admin)` in message text resolves to the correct pubkey

## Affected user (different machine, same relay/channel)
- Desktop app: channel syncs, **all of the agent's messages render**, but typing `@` in the composer never lists `Dory (web admin)`. Restarting the app does not fix it.
- Mobile app, same account: `@` picker lists `Dory (web admin)` and mentions work end to end.

## Hypotheses
- Stale per-profile cache in the desktop picker that survives app restart (old `Dory` entry dropped, renamed entry never ingested), or
- the parentheses in the new display name breaking the desktop picker's matching (mobile handles it).

## Pending details (will add in comments)
- Affected desktop app version
- Whether other agents with parenthesized names (e.g. `Nemo (chief of staff)`) appear in the affected picker — distinguishes stale-cache vs name-parsing

Possibly adjacent: during the same rename+access edit, the Desktop definition-to-runtime sync silently dropped the `respond_to` change in managed-agents.json (runtime kept `owner-only` while the definition said `anyone`; parallelism and name synced fine). Happy to split that into its own issue if useful.