docs: UI-audit fixes in CLAUDE.md, API, OpenAPI, LANES and READMEs

New params and errors (agents session_ids, sessions awaiting/from/to,
stats tool counts, event labels, cleanup dry_run/INVALID_PURGE_DAYS, lane
start slot auto/ESESSIONLIVE/EUNSUPPORTED), terminal and pane shortcuts,
the shared UI primitives, accent vs accent-solid, lazy routes and the
Settings groups. openapi.yaml regenerated.

server/openapi.js

@@ -554,6 +554,17 @@ function createOpenApiSpec() {
                 },
               },
             },
+            tool_call_count: {
+              type: "integer",
+              minimum: 0,
+              description:
+                "Exact tool calls: PreToolUse events with a tool_name, or PostToolUse ones when the session has no PreToolUse (an imported session). tools_used is a top-15 list, so its sum is not this.",
+            },
+            distinct_tool_count: {
+              type: "integer",
+              minimum: 0,
+              description: "Number of different tool names this session called.",
+            },
             error_count: {
               type: "integer",
               minimum: 0,
@@ -1363,10 +1374,14 @@ function createOpenApiSpec() {
               description: "Mark active sessions abandoned if stale for this many hours",
             },
             purge_days: {
-              type: "number",
-              minimum: 0,
+              type: "integer",
+              minimum: 1,
               description:
-                "Delete old completed/error/abandoned sessions older than this many days",
+                "Delete old completed/error/abandoned sessions older than this many days. A whole number ≥ 1, else 400 INVALID_PURGE_DAYS (a fraction would purge almost everything).",
+            },
+            dry_run: {
+              type: "boolean",
+              description: "true = answer the same counts and change nothing.",
             },
           },
         },
@@ -1379,6 +1394,11 @@ function createOpenApiSpec() {
             purged_sessions: { type: "integer" },
             purged_events: { type: "integer" },
             purged_agents: { type: "integer" },
+            dry_run: {
+              type: "boolean",
+              enum: [true],
+              description: "Present (true) only on a dry run: the counts were not applied.",
+            },
           },
         },
       },