fix(dot): label saved Dot agents and setup checks consistently

Co-Authored-By: Paperclip <noreply@paperclip.ing>

ui/src/components/AgentConfigForm.tsx

@@ -2168,6 +2168,7 @@ export function AgentConfigForm(props: AgentConfigFormProps) {
 
       {props.compactTestFeedback && showInlineAdapterTestEnvironmentFeedback && showAdapterTestEnvironmentButton && (
         <RuntimeTestCard
+          variant={isDotRunner ? "prerequisites" : "connection"}
           state={testActionPending ? "running" : testActionError || testEnvironment.error ? "fail" : testResult?.status ?? "idle"}
           result={testResult ?? null}
           error={testActionError ?? (testEnvironment.error instanceof Error ? testEnvironment.error.message : null)}

ui/src/components/RuntimeTestCard.tsx

@@ -41,7 +41,7 @@ const copy = {
 const prerequisiteCopy = {
   idle: { title: "Check prerequisites", description: "Check instance settings and public connection configuration.", action: "Check setup" },
   running: { title: "Checking prerequisites", description: "Checking instance settings and public connection configuration…", action: "Checking…" },
-  pass: { title: "Setup checks passed", description: "Complete pairing and verify event delivery before assigning work.", action: "Check again" },
+  pass: { title: "Setup checks passed", description: "Review the setup details before assigning work.", action: "Check again" },
   warn: { title: "Pairing required", description: "Create this agent, then pair it and verify event delivery.", action: "Check again" },
   fail: { title: "Prerequisite check failed", description: "Review the setup details and retry.", action: "Retry check" },
 } as const;

ui/src/pages/AgentDetail.tsx

@@ -1252,7 +1252,7 @@ export function AgentDetail() {
               {agent.adapterType === "claude_local" || agent.adapterType === "codex_local"
                 ? <img src={`/brands/${agent.adapterType === "claude_local" ? "claude" : "codex"}-color.svg`} className="size-4" alt="" />
                 : null}
-              <span>{getAdapterDisplay(agent.adapterType).label}</span><span>·</span>
+              <span>{getAdapterDisplay(agent.adapterType === "paperclip_runner" && agent.adapterConfig.provider === "openai_dot" ? "openai_dot" : agent.adapterType).label}</span><span>·</span>
               <span>{agent.title || roleLabels[agent.role] || agent.role}</span>
             </div>
           </div>
@@ -1776,7 +1776,7 @@ export function AgentOverview({
             <Link className="text-xs text-muted-foreground hover:text-foreground" to={agentDetailHref(agentRouteId, "runtime")}>Configure</Link>
           </div>
           <div className="space-y-3">
-            <SummaryRow label="Adapter"><span className="text-sm">{adapterLabels[agent.adapterType] ?? agent.adapterType}</span></SummaryRow>
+            <SummaryRow label="Adapter"><span className="text-sm">{getAdapterDisplay(agent.adapterType === "paperclip_runner" && agent.adapterConfig.provider === "openai_dot" ? "openai_dot" : agent.adapterType).label}</span></SummaryRow>
             <SummaryRow label="Model"><span className="max-w-64 truncate text-sm font-mono">{configuredModel}</span></SummaryRow>
             <SummaryRow label="Session"><span className="max-w-64 truncate text-sm font-mono">{runtimeState?.sessionDisplayId ?? runtimeState?.sessionId ?? "No session"}</span></SummaryRow>
             <SummaryRow label="Last run">