feat(research): wire tools + research workflow graph (research-workflow §2/§3)

Makes the research feature runnable end-to-end, off by default.

- config: [tools.research] (enabled, searxng_url, max_results, max_fetch_bytes).
- registration: web_search/web_fetch are built into BOTH the default and per-workspace
  tool registries when research.enabled, sharing one HTTP client threaded from Main
  (none built on the static path). Egress stays harness-enforced: web_fetch is T2
  (operator-approved) and the existing NetworkHostRule still applies.
- workflow: examples/workflows/research.toml — decompose → gather → report, with the
  three artifact schemas and prompts. Fan-out (search per sub-question, fetch per source)
  runs as repeated tool calls inside the gather stage (Correx has no parallel agents);
  per-source synthesis into the dossier is the compression step, so the report stage
  consumes summaries, never raw pages. ResearchWorkflowTest validates the graph contract.

To run: set [tools.research].enabled, register the 3 [[artifacts]], copy research.toml +
prompts + schemas into the workflows dir, start SearXNG. Launch like any workflow (the
T2 fetch approval surfaces as an approval card; the report opens in the artifact viewer).

Follow-ups (noted, not blocking): batch fetch-approval at the source-list level (§3),
a dedicated SourceFetched/LowQualityExtraction event (quality + content hash are already
in tool-result metadata), dynamic per-session egress allowlist, and the web approval client (§6).

apps/server/src/main/kotlin/com/correx/apps/server/Main.kt

@@ -195,12 +195,26 @@ fun main() {
         ?.let { Path.of(it) }
         ?: toolsConfig.workspaceRoot.takeIf { it.isNotEmpty() }?.let { Path.of(it) }
         ?: workingDir
+    // One shared HTTP client backs both the default and per-workspace registries' research tools
+    // (web_search/web_fetch). Built only when research is enabled, so the static path stays offline.
+    val researchToolConfig = com.correx.infrastructure.tools.ResearchToolConfig(
+        enabled = toolsConfig.research.enabled,
+        searxngUrl = toolsConfig.research.searxngUrl,
+        maxResults = toolsConfig.research.maxResults,
+        maxFetchBytes = toolsConfig.research.maxFetchBytes,
+        httpClient = if (toolsConfig.research.enabled) {
+            io.ktor.client.HttpClient(io.ktor.client.engine.cio.CIO)
+        } else {
+            null
+        },
+    )
     val toolRegistry = InfrastructureModule.createToolRegistry(
         buildToolConfig(
             workspaceRoot,
             workingDir,
             shellAllowedExecutables,
             toolsConfig,
+            researchToolConfig,
         ),
     )
     val toolExecutor = InfrastructureModule.createToolExecutor(
@@ -228,7 +242,7 @@ fun main() {
 
     val wsToolRegistryProvider = WorkspaceToolRegistryProvider { workspace ->
         val wsRegistry = InfrastructureModule.createToolRegistry(
-            buildToolConfigForWorkspace(workspace, shellAllowedExecutables, toolsConfig),
+            buildToolConfigForWorkspace(workspace, shellAllowedExecutables, toolsConfig, researchToolConfig),
         )
         val wsExecutor = DispatchingToolExecutor(wsRegistry)
         WorkspaceTools(registry = wsRegistry, executor = wsExecutor)
@@ -626,6 +640,7 @@ private fun buildToolConfig(
     workingDir: Path,
     shellAllowedExecutables: Set<String>,
     toolsConfig: com.correx.core.config.ToolsConfig,
+    research: com.correx.infrastructure.tools.ResearchToolConfig,
 ): ToolConfig {
     val allowed = setOf(workspaceRoot, workingDir)
     return ToolConfig(
@@ -648,6 +663,7 @@ private fun buildToolConfig(
             allowedPaths = allowed,
             workingDir = workingDir,
         ),
+        research = research,
     )
 }
 
@@ -655,7 +671,9 @@ private fun buildToolConfigForWorkspace(
     workspace: WorkspaceContext,
     shellAllowedExecutables: Set<String>,
     toolsConfig: com.correx.core.config.ToolsConfig,
+    research: com.correx.infrastructure.tools.ResearchToolConfig,
 ): ToolConfig = ToolConfig(
+    research = research,
     shell = ShellConfig(
         enabled = toolsConfig.shellEnabled,
         allowedExecutables = shellAllowedExecutables,