feat(providers): an OpenAI-compatible preset for any vLLM, LM Studio or gateway URL

Step 8 of the provider refactor plan, a new provider made of one record.
'custom' runs on @ai-sdk/openai-compatible with <think> extraction, merges
system messages (open-source chat templates reject several), has no default
URL (so a key alone does not count as connected, and the chat endpoint is
shown under the URL field) and lists models from its /models. Server side:
CUSTOM_API_KEY and CUSTOM_BASE_URL, ADMIN_CUSTOM_* in the admin panel.
env.example and the three provider docs gained a section; the picker count
in the e2e test is 25 and a new e2e test walks through the preset. The
behavior snapshot gained the new provider's 146 rows; its two 'No AI provider
configured' rows list CUSTOM_API_KEY now.

tests/unit/provider-matrix.test.ts

@@ -158,6 +158,7 @@ const MATRIX_PROVIDERS: ProviderName[] = [
     "novita",
     "mimo",
     "atlascloud",
+    "custom",
 ]
 
 /** The model id each provider runs in the matrix (the first suggested one) */
@@ -186,6 +187,7 @@ const MATRIX_MODEL_IDS: Record<ProviderName, string> = {
     novita: "minimax/minimax-m3",
     mimo: "mimo-v2.5-pro",
     atlascloud: "qwen/qwen3.5-flash",
+    custom: "test-model",
 }
 
 /** Model ids whose providerOptions the snapshot records for openai and google */
@@ -449,7 +451,7 @@ describe("provider behavior snapshot", () => {
     })
 
     it("matches the recorded behavior", async () => {
-        // The matrix: 24 providers, 16 shapes, 9 environments
+        // The matrix: 25 providers, 16 shapes, 9 environments
         for (const provider of MATRIX_PROVIDERS) {
             await matrix(provider, MATRIX_MODEL_IDS[provider])
         }