Improve model picker UX (#1180)

1. Show less common AI providers (secondary) in submenu
2. Show $ signs for rough cost guide
3. Show "Pro" for supported AI providers with Pro is enabled

    
<!-- This is an auto-generated description by cubic. -->
---

## Summary by cubic
Improves the Model Picker UX by grouping less-used providers under an
“Other AI providers” submenu and adding clear cost and Pro indicators.
This makes picking models faster and more informative.

- **New Features**
- Grouped secondary providers under “Other AI providers” using a new
provider.secondary flag (Azure marked secondary).
- Added rough cost hints: models can set dollarSigns and the UI shows a
“$” badge accordingly.
- Shows a “Pro” badge on supported cloud providers when Pro is enabled;
added a “Custom” badge for custom providers.
- Extended types: LanguageModelProvider.secondary and
LanguageModel.dollarSigns; populated values across OpenAI, Anthropic,
Google, and OpenRouter.

<!-- End of auto-generated description by cubic. -->

e2e-tests/engine.spec.ts

@@ -26,11 +26,11 @@ testSkipIfWindows(
   },
 );
 
-testSkipIfWindows("send message to engine - openai gpt-4.1", async ({ po }) => {
+testSkipIfWindows("send message to engine - openai gpt-5", async ({ po }) => {
   await po.setUpDyadPro();
   // By default, it's using auto which points to Flash 2.5 and doesn't
   // use engine.
-  await po.selectModel({ provider: "OpenAI", model: "GPT 4.1" });
+  await po.selectModel({ provider: "OpenAI", model: "GPT 5" });
   await po.sendPrompt("[dump] tc=turbo-edits");
 
   await po.snapshotServerDump("request");

e2e-tests/helpers/test_helper.ts

@@ -703,6 +703,7 @@ export class PageObject {
 
   async selectTestAzureModel() {
     await this.page.getByRole("button", { name: "Model: Auto" }).click();
+    await this.page.getByText("Other AI providers").click();
     await this.page.getByText("Azure OpenAI", { exact: true }).click();
     await this.page.getByText("GPT-5", { exact: true }).click();
   }

e2e-tests/snapshots/engine.spec.ts_send-message-to-engine---openai-gpt-5-1.txt

@@ -1,8 +1,7 @@
 {
   "body": {
-    "model": "gpt-4.1",
-    "max_tokens": 32768,
-    "temperature": 0,
+    "model": "gpt-5",
+    "temperature": 1,
     "messages": [
       {
         "role": "system",