[codex] Bundle local branch fixes from PAP-10032 (#6604)

## Thinking Path

> - Paperclip orchestrates AI agents for zero-human companies.
> - This branch accumulated multiple already-tested control-plane,
adapter runtime, invite, workspace, plugin, and UI quality fixes on the
primary Paperclip checkout.
> - `origin/master` advanced while those commits were still local, so
the branch needed to be preserved and reconciled before review.
> - Splitting the branch commit-by-commit against the new base produced
overlapping conflicts with recently merged upstream PRs.
> - This pull request keeps the remaining branch as one standalone PR
because the final diff is 38 files after removing screenshot artifacts,
under Greptile's 100-file cap, and can be merged independently after
review.
> - The benefit is that none of the local work is lost, the branch is
now based on current `origin/master`, and reviewers can evaluate the
reconciled changes in one place.

## What Changed

- Merged the local accumulated branch with current `origin/master` and
resolved the invite-flow overlaps from the newer upstream companies
query helper.
- Preserved the local fixes for invite existing-member behavior, invite
link copy fallback, reusable workspace selection, worktree auth, static
SPA fallback, markdown wrapping, plugin slot registration, cloud
upstream UX/server polish, project sorting, and related tests.
- Removed screenshot artifacts from the PR per review request.
- Kept the PR under the requested file limit: 38 files changed, with no
`pnpm-lock.yaml` or `.github/workflows/*` changes.

## Verification

- `NODE_ENV=test pnpm exec vitest run
ui/src/pages/CompanyInvites.test.tsx ui/src/pages/InviteLanding.test.tsx
ui/src/pages/Projects.test.tsx ui/src/plugins/slots.test.ts
ui/src/components/MarkdownBody.test.tsx
server/src/__tests__/invite-accept-existing-member.test.ts
server/src/__tests__/static-index-html.test.ts
server/src/__tests__/execution-workspaces-service.test.ts
server/src/__tests__/better-auth.test.ts
server/src/__tests__/worktree-config.test.ts`
- `NODE_ENV=test pnpm --filter @paperclipai/ui typecheck`
- `NODE_ENV=test pnpm --filter @paperclipai/server typecheck`
- Confirmed `git diff --name-only origin/master...HEAD | wc -l` is `38`.
- Confirmed no PR diff entries match `pnpm-lock.yaml`,
`.github/workflows/*`, or `screenshots/*`.

## Risks

- Medium review risk because this is a bundled rescue PR rather than
several narrow feature PRs.
- Invite flow and company cache behavior overlapped with newer upstream
changes; the merge resolution intentionally keeps the shared
`companiesListQueryOptions` helper while preserving local
existing-member invite behavior.
- Visual review evidence is no longer attached in-repo because
screenshots were removed from this PR per review request.

> For core feature work, check [`ROADMAP.md`](ROADMAP.md) first and
discuss it in `#dev` before opening the PR. Feature PRs that overlap
with planned core work may need to be redirected — check the roadmap
first. See `CONTRIBUTING.md`.

## Model Used

- OpenAI Codex, GPT-5-based coding agent, with repository tool access,
terminal execution, and git/GitHub CLI operations.

## 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 checked ROADMAP.md and confirmed this PR does not duplicate
planned core work
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [x] UI screenshots were intentionally removed from this PR per review
request
- [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>
Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>
Co-authored-by: CodexCoder <codexcoder@paperclip.local>

packages/shared/src/types/workspace-runtime.ts

@@ -168,7 +168,11 @@ export interface ExecutionWorkspaceSummary {
   id: string;
   name: string;
   mode: Exclude<ExecutionWorkspaceMode, "inherit" | "reuse_existing" | "agent_default"> | "adapter_managed" | "cloud_sandbox";
+  status: ExecutionWorkspaceStatus;
+  cwd: string | null;
+  branchName: string | null;
   projectWorkspaceId: string | null;
+  lastUsedAt: Date;
 }
 
 export interface ExecutionWorkspace {