[codex] improve issue and routine UI responsiveness (#3744)

## Thinking Path

> - Paperclip orchestrates AI agents for zero-human companies
> - Operators rely on issue, inbox, and routine views to understand what
the company is doing in real time
> - Those views need to stay fast and readable even when issue lists,
markdown comments, and run metadata get large
> - The current branch had a coherent set of UI and live-update
improvements spread across issue search, issue detail rendering, routine
affordances, and workspace lookups
> - This pull request groups those board-facing changes into one
standalone branch that can merge independently of the heartbeat/runtime
work
> - The benefit is a faster, clearer issue and routine workflow without
changing the underlying task model

## What Changed

- Show routine execution issues by default and rename the filter to
`Hide routine runs` so the default state no longer looks like an active
filter.
- Show the routine name in the run dialog and tighten the issue
properties pane with a workspace link, copy-on-click behavior, and an
inline parent arrow.
- Reduce issue detail rerenders, keep queued issue chat mounted, improve
issues page search responsiveness, and speed up issues first paint.
- Add inbox "other search results", refresh visible issue runs after
status updates, and optimize workspace lookups through summary-mode
execution workspace queries.
- Improve markdown wrapping and scrolling behavior for long strings and
self-comment code blocks.
- Relax the markdown sanitizer assertion so the test still validates
safety after the new wrap-friendly inline styles.

## Verification

- `pnpm vitest run ui/src/components/IssuesList.test.tsx
ui/src/lib/inbox.test.ts ui/src/pages/Issues.test.tsx
ui/src/context/BreadcrumbContext.test.tsx
ui/src/context/LiveUpdatesProvider.test.ts
ui/src/components/MarkdownBody.test.tsx
ui/src/api/execution-workspaces.test.ts
server/src/__tests__/execution-workspaces-routes.test.ts`

## Risks

- This touches several issue-facing UI surfaces at once, so regressions
would most likely show up as stale rendering, search result mismatches,
or small markdown presentation differences.
- The workspace lookup optimization depends on the summary-mode route
shape staying aligned between server and UI.

## Model Used

- OpenAI Codex, GPT-5-based coding agent in the Codex CLI environment.
Exact backend model deployment ID was not exposed in-session.
Tool-assisted editing and shell execution were used.

## Checklist

- [x] I have included a thinking path that traces from project context
to this change
- [x] I have specified the model used (with version and capability
details)
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [ ] If this change affects the UI, I have included before/after
screenshots
- [x] I have updated relevant documentation to reflect my changes
- [x] I have considered and documented any risks above
- [x] I will address all Greptile and reviewer comments before
requesting merge

---------

Co-authored-by: Paperclip <noreply@paperclip.ing>

ui/src/lib/inbox.ts

@@ -87,6 +87,16 @@ export interface InboxWorkItemGroup {
   items: InboxWorkItem[];
 }
 
+export type InboxSearchSection = "none" | "archived" | "other";
+
+export interface InboxGroupedSection {
+  key: string;
+  label: string | null;
+  displayItems: InboxWorkItem[];
+  childrenByIssueId: Map<string, Issue[]>;
+  searchSection: InboxSearchSection;
+}
+
 export interface InboxKeyboardGroupSection {
   key: string;
   displayItems: InboxWorkItem[];
@@ -142,7 +152,7 @@ function normalizeIssueFilterState(value: unknown): IssueFilterState {
     labels: normalizeStringArray(candidate.labels),
     projects: normalizeStringArray(candidate.projects),
     workspaces: normalizeStringArray(candidate.workspaces),
-    showRoutineExecutions: candidate.showRoutineExecutions === true,
+    hideRoutineExecutions: candidate.hideRoutineExecutions === true,
   };
 }
 
@@ -367,14 +377,14 @@ export function shouldResetInboxWorkspaceGrouping(
 
 export function shouldIncludeRoutineExecutionIssue(
   issue: Pick<Issue, "originKind">,
-  showRoutineExecutions: boolean,
+  hideRoutineExecutions: boolean,
 ): boolean {
-  return showRoutineExecutions || issue.originKind !== "routine_execution";
+  return !hideRoutineExecutions || issue.originKind !== "routine_execution";
 }
 
-export function filterInboxIssues(issues: Issue[], showRoutineExecutions: boolean): Issue[] {
-  if (showRoutineExecutions) return issues;
-  return issues.filter((issue) => shouldIncludeRoutineExecutionIssue(issue, showRoutineExecutions));
+export function filterInboxIssues(issues: Issue[], hideRoutineExecutions: boolean): Issue[] {
+  if (!hideRoutineExecutions) return issues;
+  return issues.filter((issue) => shouldIncludeRoutineExecutionIssue(issue, hideRoutineExecutions));
 }
 
 export function matchesInboxIssueSearch(
@@ -916,6 +926,31 @@ export function buildInboxNesting(items: InboxWorkItem[]): {
   return { displayItems, childrenByIssueId };
 }
 
+export function buildGroupedInboxSections(
+  items: InboxWorkItem[],
+  groupBy: InboxWorkItemGroupBy,
+  workspaceGrouping: InboxWorkspaceGroupingOptions,
+  options?: { keyPrefix?: string; searchSection?: InboxSearchSection; nestingEnabled?: boolean },
+): InboxGroupedSection[] {
+  const keyPrefix = options?.keyPrefix ?? "";
+  const searchSection = options?.searchSection ?? "none";
+  const nestingEnabled = options?.nestingEnabled ?? false;
+
+  return groupInboxWorkItems(items, groupBy, workspaceGrouping).map((group) => {
+    const nestedGroup = nestingEnabled && group.items.some((item) => item.kind === "issue")
+      ? buildInboxNesting(group.items)
+      : { displayItems: group.items, childrenByIssueId: new Map<string, Issue[]>() };
+
+    return {
+      key: `${keyPrefix}${group.key}`,
+      label: group.label,
+      displayItems: nestedGroup.displayItems,
+      childrenByIssueId: nestedGroup.childrenByIssueId,
+      searchSection,
+    };
+  });
+}
+
 export function getInboxWorkItemKey(item: InboxWorkItem): string {
   if (item.kind === "issue") return `issue:${item.issue.id}`;
   if (item.kind === "approval") return `approval:${item.approval.id}`;