Desktop: removed personal agent cannot be re-added from Channel members picker

## Summary

After a channel owner removes a personal Desktop-managed agent from a private DM/channel, Buzz Desktop's **Channel members** picker cannot find that agent again by either display name or exact 64-character pubkey. The owner therefore has no UI path to re-add the agent.

## Reproduction

1. Start with a private DM/channel containing the owner and one or more personal managed agents.
2. Remove one personal agent from the channel.
3. Click the members button in the channel header to open **Channel members**.
4. Search for the removed agent by its exact display name.
5. Observe: **No matching people or agents.**
6. Replace the search with the agent's exact 64-character hex pubkey.
7. Observe: **No matching people or agents.**

## Observed behavior

- The channel history records that the agent was previously added and then removed.
- The channel is now private with one remaining member.
- The member picker returns no result for either the agent name or exact pubkey.
- The relay still resolves the same pubkey to the expected agent profile:
`buzz users get --pubkey ` returns `display_name: "Alexander the Great"`.
- Self-join is correctly rejected because the channel is private, so there is no fallback path for the agent.

## Expected behavior

A channel owner should be able to find and re-add a previously removed personal managed agent from the **Channel members** picker. Exact-pubkey lookup should work even if display-name indexing or local managed-agent state is stale.

## Evidence

- Channel state/history after removal:
http://37.27.203.77/media/ddf936d5442498a7b5990c9dd8feafc3275157c35e0257e28970607cf9334538.png
- Display-name lookup returns no match:
http://37.27.203.77/media/2022885df8e1d822709e56413afe55c77087cbb1abed7d893b387df753356580.png
- Exact-pubkey lookup returns no match:
http://37.27.203.77/media/7087541496f437e1391bfb4de3302f6a258ab7404a081f86afcc2d018be9a9aa.png

## Environment

- Buzz Desktop on macOS
- Hosted Buzz relay
- Observed 2026-08-04 (America/Los_Angeles)
- Desktop version not captured

## Related but distinct

- #2423 covers identity desynchronization after rename/re-add, whereas this report is the earlier failure: the removed personal agent cannot be selected for re-add at all.
- #2987 covers the add-member gate for external/non-managed agents; this case affects the owner's own personal Desktop-managed agent.
- #3577 describes removed agents remaining mentionable and being silently re-added; this report shows the opposite member-picker behavior when intentionally trying to re-add one.