Fix (review): seat picker must surface the skill the run resolves

Adversarial review found a display-vs-run mismatch: the seat picker collapses the library to the
first row per key, but ListSkills ordered by version only — so for a key the org authored alongside
a higher-versioned builtin, the picker showed/flagged the builtin while the run injected the org's
own skill. ListSkills now orders the same way the run-time catalog resolves (Published-first,
org-owned-over-builtin, then latest version with the same Ordinal comparison), computed in-memory so
the version tiebreak can't diverge from SkillCatalog. The run itself was already correct; this aligns
what the operator sees with what executes. No client change needed.

SkillRunScopingTests now also asserts the library's first row for a key the org authored is the
org-owned Published row, not the builtin.

Verified: skills test subset 4/4 (full suite green pre-merge).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

tests/TeamUp.IntegrationTests/SkillRunScopingTests.cs

@@ -32,6 +32,8 @@ public sealed class SkillRunScopingTests(PostgresFixture postgres) : IClassFixtu
 
     private sealed record SyncResult(int Indexed);
 
+    private sealed record SkillSummary(string SkillKey, string Name, string Version, string Status);
+
     private sealed record RunResponse(
         Guid Id, Guid SeatId, Guid WorkItemId, Guid? AgentId, string Status,
         string? ActionType, string? ActionRisk, string? Prompt, string? Output, string? Error);
@@ -125,6 +127,14 @@ public sealed class SkillRunScopingTests(PostgresFixture postgres) : IClassFixtu
         Assert.Contains(OrgABody, done.Prompt);
         // …and another org's same-key skill never leaked across the tenant boundary.
         Assert.DoesNotContain(OrgBPoison, done.Prompt);
+
+        // The seat picker collapses to the first row per key — that row must be the one the run
+        // resolved (the org's own, not the builtin), so seat configuration matches execution.
+        var library = await client.GetFromJsonAsync<List<SkillSummary>>(
+            $"/api/skills/?organizationId={owner.OrganizationId}");
+        var firstImpl = library!.First(s => s.SkillKey == "code-implementation");
+        Assert.Equal("ACME Code Impl", firstImpl.Name);
+        Assert.Equal("Published", firstImpl.Status);
     }
 
     private static async Task SeedSkillAsync(TeamUpWebFactory factory, Guid orgId, string key, string body)