refactor(search): fold zai-search into the glm provider

The separate zai-search entry showed "No connections" on the web search
page because credentials live on the `glm` connection, not on it. Every
other provider that does both chat and search (antigravity, kimi, xai,
gemini) declares webSearch on the provider itself, so do the same here.

- glm gains serviceKinds ["llm", "webSearch"] and the MCP searchConfig
- the request builder / normalizer move from "zai-search" to "glm"
- drop the zai-search registry entry and its svg logo, which also
  removes the only need for svg logo support in getProviderIconSrc

ollama-search keeps its own entry and credentialFallback: its search
endpoint is unrelated to the ollama chat transport.

open-sse/handlers/search/callers.js

@@ -394,12 +394,12 @@ function buildOllamaSearchRequest(config, params) {
   };
 }
 
-// ── Z.AI Coding plan MCP web_search_prime ─────────────────────────────────
+// ── GLM Coding plan MCP web_search_prime ──────────────────────────────────
 // POST https://api.z.ai/api/mcp/web_search_prime/mcp
 // JSON-RPC envelope: { jsonrpc, id, method: "tools/call",
 //   params: { name: "web_search_prime", arguments: { search_query, count } } }
 // Response: { result: { content: [{ type: "text", text: "<json>" }] } }
-function buildZaiSearchRequest(config, params) {
+function buildGlmSearchRequest(config, params) {
   const body = {
     jsonrpc: "2.0",
     id: `9r-${Date.now()}`,
@@ -437,7 +437,7 @@ const BUILDERS = {
   "searxng": buildSearxngRequest,
   "xquik": buildXquikRequest,
   "ollama-search": buildOllamaSearchRequest,
-  "zai-search": buildZaiSearchRequest,
+  "glm": buildGlmSearchRequest,
 };
 
 /**

open-sse/handlers/search/normalizers.js

@@ -257,7 +257,7 @@ function normalizeOllamaSearch(data, _query, _searchType) {
   return { results, totalResults: results.length };
 }
 
-function normalizeZaiSearch(data, _query, _searchType) {
+function normalizeGlmSearch(data, _query, _searchType) {
   const now = new Date().toISOString();
   // MCP envelope: { result: { content: [{ type: "text", text: "<json>" }] } }
   let payload = data;
@@ -270,7 +270,7 @@ function normalizeZaiSearch(data, _query, _searchType) {
     : Array.isArray(payload) ? payload
     : [];
   const results = items.map((item, idx) =>
-    makeResult("zai-search", {
+    makeResult("glm", {
       title: item.title,
       url: item.link || item.url,
       snippet: item.content || "",
@@ -295,7 +295,7 @@ const NORMALIZERS = {
   "searxng": normalizeSearxng,
   "xquik": normalizeXquik,
   "ollama-search": normalizeOllamaSearch,
-  "zai-search": normalizeZaiSearch,
+  "glm": normalizeGlmSearch,
 };
 
 /**