Normalize adapter display labels (#8913)

## Thinking Path

> - Paperclip is the open source app people use to manage AI agents for
work.
> - Adapter names are part of the board-facing agent setup and
management experience.
> - The product now treats adapters as harnesses, while execution
environments are modeled separately.
> - Several built-in adapter labels still carried legacy local wording
from the older harness-by-environment model.
> - That wording makes the UI noisier and implies a distinction users no
longer need to reason about.
> - This pull request normalizes adapter display labels while keeping
persisted adapter type identifiers unchanged.
> - The benefit is clearer adapter selection and management copy without
a database migration.

## Linked Issues or Issue Description

No public GitHub issue was found for this exact cleanup.

Related public PRs:

- Supersedes #8910, an earlier branch for the same cleanup that did not
include the later docs/gateway/Cursor alignment.
- Refs #8819, which is related display-registry work for external
multi-segment adapter labels, but not a duplicate of this built-in label
cleanup.

Feature request details:

- Subsystem affected: Cross-cutting (`ui/`, `packages/adapters`, and
docs).
- Problem or motivation: user-facing adapter names include legacy local
qualifiers even though adapters map to harnesses and environments are
first-class elsewhere.
- Proposed solution: remove the legacy local wording from built-in
display labels, keep machine-readable adapter type ids unchanged, and
keep gateway disambiguation where it is useful.
- Alternatives considered: changing persisted adapter type ids was ruled
out because it would create migration and compatibility risk; one-off UI
replacements were ruled out because the display registry is already the
correct central label boundary.
- Roadmap alignment: this is small adapter UX polish, not a new
roadmap-level core feature.

## What Changed

- Updated the adapter display registry so known adapter labels are final
and no built-in local adapter renders a legacy local suffix.
- Preserved clean derived labels for unknown plugin local types while
keeping gateway disambiguation for unknown gateway types.
- Updated `AdapterManager` to prefer registry labels when the server
reports raw adapter type ids for built-ins.
- Removed legacy local wording from built-in adapter metadata labels in
UI and adapter packages.
- Aligned Cursor adapter metadata with the central display registry
label.
- Updated adapter docs and Storybook fixtures to match the new display
names.
- Added focused registry coverage for built-in labels and unknown plugin
suffix behavior.

## Verification

- `pnpm check:tokens`
- `git diff --check origin/master...fix/adapter-display-labels`
- Patch-addition scan for added secrets, private paths, and internal
links: no matches.
- GitHub duplicate search for open adapter-label/local-suffix issues and
PRs; #8910 was identified as the older superseded public PR.
- `pnpm exec vitest run
ui/src/adapters/adapter-display-registry.test.ts`
- `pnpm --filter @paperclipai/ui typecheck`
- Stale-label scan found no remaining user-facing display-label
suffixes; remaining local wording is operational/test terminology such
as adapter ids, docs about running locally, and test descriptions.

## Risks

Low risk. The change is display-label and documentation focused, and
adapter type ids remain unchanged. The main risk is ambiguous gateway
naming, mitigated by keeping explicit gateway labels where variants need
disambiguation.

## Model Used

OpenAI GPT-5 via Codex, tool-enabled coding agent in a local repository
workspace. Context window size is not exposed by this environment.

## 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 searched GitHub for duplicate or related PRs and linked
them above
- [x] I have either (a) linked existing issues with `Fixes: #` / `Closes
#` / `Refs #` OR (b) described the issue in-PR following the relevant
issue template
- [x] I have not referenced internal/instance-local Paperclip issues or
links (only public GitHub `#NNN` / `github.com/paperclipai/paperclip`
URLs)
- [x] My branch name describes the change (e.g. `docs/...`, `fix/...`)
and contains no internal Paperclip ticket id or instance-derived details
- [x] I have run tests locally and they pass
- [x] I have added or updated tests where applicable
- [x] I have updated relevant documentation to reflect my changes
- [x] I have considered and documented any risks above
- [x] All Paperclip CI gates are green
- [x] Greptile is 5/5 with no open P2s, recommendations, or follow-ups
- [x] I will address all Greptile and reviewer comments before
requesting merge

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

docs/adapters/claude-local.md

@@ -1,5 +1,5 @@
 ---
-title: Claude Local
+title: Claude Code
 summary: Claude Code local adapter setup and configuration
 ---
 

docs/adapters/codex-local.md

@@ -1,5 +1,5 @@
 ---
-title: Codex Local
+title: Codex
 summary: OpenAI Codex local adapter setup and configuration
 ---
 

docs/adapters/creating-an-adapter.md

@@ -54,7 +54,7 @@ my-adapter/                   # external plugin
 
 ```ts
 export const type = "my_agent";        // snake_case, globally unique
-export const label = "My Agent (local)";
+export const label = "My Agent";
 export const models = [
   { id: "model-a", label: "Model A" },
 ];

docs/adapters/external-adapters.md

@@ -116,7 +116,7 @@ The plugin loader calls `createServerAdapter()` from your package root. This fun
 
 ```ts
 export const type = "my_adapter";     // snake_case, globally unique
-export const label = "My Agent (local)";
+export const label = "My Agent";
 
 export const models = [
   { id: "model-a", label: "Model A" },

docs/adapters/gemini-local.md

@@ -1,5 +1,5 @@
 ---
-title: Gemini Local
+title: Gemini CLI
 summary: Gemini CLI local adapter setup and configuration
 ---
 

docs/adapters/overview.md

@@ -18,13 +18,13 @@ When a heartbeat fires, Paperclip:
 
 | Adapter | Type Key | Description |
 |---------|----------|-------------|
-| [Claude Local](/adapters/claude-local) | `claude_local` | Runs Claude Code CLI locally |
-| [Codex Local](/adapters/codex-local) | `codex_local` | Runs OpenAI Codex CLI locally |
-| [Gemini Local](/adapters/gemini-local) | `gemini_local` | Runs Gemini CLI locally (experimental — adapter package exists, not yet in stable type enum) |
-| OpenCode Local | `opencode_local` | Runs OpenCode CLI locally (multi-provider `provider/model`) |
+| [Claude Code](/adapters/claude-local) | `claude_local` | Runs Claude Code CLI locally |
+| [Codex](/adapters/codex-local) | `codex_local` | Runs OpenAI Codex CLI locally |
+| [Gemini CLI](/adapters/gemini-local) | `gemini_local` | Runs Gemini CLI locally (experimental — adapter package exists, not yet in stable type enum) |
+| OpenCode | `opencode_local` | Runs OpenCode CLI locally (multi-provider `provider/model`) |
 | Cursor | `cursor` | Runs Cursor in background mode |
-| Pi Local | `pi_local` | Runs an embedded Pi agent locally |
-| Hermes Local | `hermes_local` | Runs the local Hermes CLI through `@paperclipai/hermes-paperclip-adapter` |
+| Pi | `pi_local` | Runs an embedded Pi agent locally |
+| Hermes | `hermes_local` | Runs the local Hermes CLI through `@paperclipai/hermes-paperclip-adapter` |
 | Hermes Gateway | `hermes_gateway` | Calls an already-running Hermes API server through `@paperclipai/hermes-paperclip-adapter/gateway` |
 | OpenClaw Gateway | `openclaw_gateway` | Connects to an OpenClaw gateway endpoint |
 | [Process](/adapters/process) | `process` | Executes arbitrary shell commands |
@@ -49,7 +49,7 @@ These adapters ship as standalone npm packages and are installed via the plugin
 
 | Adapter | Package | Type Key | Description |
 |---------|---------|----------|-------------|
-| Droid Local | `@henkey/droid-paperclip-adapter` | `droid_local` | Runs Factory Droid locally |
+| Droid | `@henkey/droid-paperclip-adapter` | `droid_local` | Runs Factory Droid locally |
 
 ## External Adapters