Picker: share PR #218's guild_name field and its no-fallback-after-unlink rule

A server an org explicitly unlinked (unlinked_at) must not fall back to the
default org in the picker either, or the founding org could stream into it.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

drb-c2-core/tests/test_discord_web_picker.py

@@ -74,7 +74,7 @@ def test_directory_push_keeps_org_link(fs):
     run(web.put_guild_directory("100", body, {"service": True}))
     g = fs.get("discord_guilds", "100")
     assert g["org_id"] == ORG
-    assert g["name"] == "Fire Co. 7 (renamed)"
+    assert g["guild_name"] == "Fire Co. 7 (renamed)"
     assert [c["channel_id"] for c in g["voice_channels"]] == ["1003"]
 
 
@@ -112,6 +112,10 @@ def test_options_unlinked_fallback_follows_bot_rule(fs, monkeypatch):
     got = {g["guild_id"]: g for g in run(web.join_options("n1", OWNER))["guilds"]}
     assert got["300"]["linked"] is False
     assert "200" not in got
+    # An org that explicitly unlinked its server (PR #218) never falls back.
+    fs.put("discord_guilds", "300", {"guild_id": "300", "org_id": None, "unlinked_at": "2026-10-04T00:00:00+00:00",
+                                     "guild_name": "Unlinked", "voice_channels": []})
+    assert "300" not in [g["guild_id"] for g in run(web.join_options("n1", OWNER))["guilds"]]
 
 
 def test_options_other_org_node_is_404(fs):