refactor(tool-provider): rename web_search to exa_web_search, drop XOR toggle (#19969)

## Summary

- Today `WEB_SEARCH_PREFER_NATIVE` forces a **mutual exclusion**: either
the custom Exa tool preloads as `web_search` or the SDK-native
`web_search` binds. Same name, different backends.
- This PR lets them **coexist**. Custom Exa becomes `exa_web_search`;
native keeps `web_search`. The model picks based on tool descriptions.
- `WEB_SEARCH_PREFER_NATIVE` and `shouldUseNativeSearch()` are deleted.
Exa enablement follows `WEB_SEARCH_DRIVER` (existing). Native enablement
follows the agent's `modelConfiguration.webSearch.enabled` (existing).

## Key changes

**Config / service**
- Deleted `WEB_SEARCH_PREFER_NATIVE` (config-variables.ts)
- Deleted `WebSearchService.shouldUseNativeSearch()`
- `WebSearchService.isEnabled()` unchanged — still gates Exa
availability

**Custom tool rename**
- `ActionToolProvider.toolMap`: `'web_search'` → `'exa_web_search'`
- Descriptor name matches
- `WebSearchTool.description` rewritten to position Exa as
structured/entity-aware, complementary to native

**Native tool binder**
- `NativeToolBinder.bind()` drops the `shouldUseNativeSearch` gate.
Per-agent `modelConfiguration.webSearch.enabled` (inside
`getNativeModelTools`) stays authoritative.

**Chat**
- Preload list now always includes `exa_web_search` —
`ActionToolProvider` silently skips the descriptor when Exa is disabled,
so `getToolsByName` degrades gracefully
- Native tools always attempted; returns empty ToolSet when the model
doesn't support them
- `directTools = { ...preloadedTools, ...nativeSearchTools }` — both
present when both enabled
- `billNativeWebSearchUsage` called unconditionally (the function
already short-circuits on count ≤ 0)

**Workflow agent**
- Same unconditional billing pattern
- `WebSearchService` dependency removed

**System prompt**
- Dropped the special-cased `web_search` branch. Preloaded tools list
uniformly now.

**Frontend**
- `exa_web_search` reuses the same "Searching the web for X" display as
native
- Test coverage added

## Billing isolation (verified)

- `countNativeWebSearchCallsFromSteps` counts `toolName ===
'web_search'` only. After the rename, only native calls match. Exa calls
(`exa_web_search`) are billed separately via
`WebSearchService.emitUsageEvent` inside `search()`.
- No double-billing path.

## Behavior deltas (intended)

| Scenario | Before | After |
|---|---|---|
| Anthropic model + Exa enabled + PREFER_NATIVE=true | native only |
**both** |
| Anthropic + Exa enabled + PREFER_NATIVE=false | Exa only (as
`web_search`) | **both** |
| Non-native model + Exa enabled | Exa as `web_search` | Exa as
`exa_web_search` |
| Any model + Exa disabled + native supported | native only | native
only |
| Workflow agent with `webSearch.enabled=true` + Anthropic + Exa enabled
| native only | **both** |

## Known regression (accepted)

Customers who set `WEB_SEARCH_PREFER_NATIVE=false` to force Exa-only
will now **also** see native `web_search` if the model supports it.
There's no chat-level kill switch after this PR. Per discussion, this is
accepted — future model-level capability gating (in the model JSON) will
be the right place for that control.

## Stats

- 10 files, +63 / −73 (net deletion)
- Typecheck clean (server: 7 pre-existing unrelated, front: 13
pre-existing unrelated — zero new either side)
- Prettier clean

## Test plan

- [ ] `npx nx typecheck twenty-server` and `npx nx typecheck
twenty-front` pass
- [ ] With Anthropic + Exa enabled: chat shows both `web_search` and
`exa_web_search` in preloaded list; model can call either
- [ ] With Anthropic + Exa disabled: chat shows only native `web_search`
- [ ] With non-native model + Exa enabled: chat shows only
`exa_web_search`
- [ ] Workflow agent with `modelConfiguration.webSearch.enabled=true` +
Exa enabled: both available
- [ ] Billing: native calls billed via `billNativeWebSearchUsage`; Exa
calls billed via `WebSearchService.emitUsageEvent`; no double-billing
- [ ] Frontend: `exa_web_search` renders "Searching the web for X" the
same as `web_search`

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

packages/twenty-server/src/modules/workflow/workflow-executor/workflow-actions/ai-agent/ai-agent.workflow-action.ts

@@ -10,7 +10,6 @@ import { AgentAsyncExecutorService } from 'src/engine/metadata-modules/ai/ai-age
 import { AgentEntity } from 'src/engine/metadata-modules/ai/ai-agent/entities/agent.entity';
 import { AiBillingService } from 'src/engine/metadata-modules/ai/ai-billing/services/ai-billing.service';
 import { UsageOperationType } from 'src/engine/core-modules/usage/enums/usage-operation-type.enum';
-import { WebSearchService } from 'src/engine/core-modules/web-search/web-search.service';
 import { AUTO_SELECT_SMART_MODEL_ID } from 'twenty-shared/constants';
 import {
   WorkflowStepExecutorException,
@@ -28,7 +27,6 @@ export class AiAgentWorkflowAction implements WorkflowAction {
   constructor(
     private readonly aiAgentExecutionService: AgentAsyncExecutorService,
     private readonly aiBillingService: AiBillingService,
-    private readonly webSearchService: WebSearchService,
     private readonly workflowExecutionContextService: WorkflowExecutionContextService,
     @InjectRepository(AgentEntity)
     private readonly agentRepository: Repository<AgentEntity>,
@@ -101,13 +99,13 @@ export class AiAgentWorkflowAction implements WorkflowAction {
       userWorkspaceId,
     );
 
-    if (this.webSearchService.shouldUseNativeSearch()) {
-      this.aiBillingService.billNativeWebSearchUsage(
-        nativeWebSearchCallCount,
-        workspaceId,
-        userWorkspaceId,
-      );
-    }
+    // billNativeWebSearchUsage short-circuits when count <= 0, so calling
+    // unconditionally is safe regardless of whether native search fired.
+    this.aiBillingService.billNativeWebSearchUsage(
+      nativeWebSearchCallCount,
+      workspaceId,
+      userWorkspaceId,
+    );
 
     return {
       result,