feat: add search/filter and custom model ID support to model selector

[pablospe]

Summary

• Add search/filter input to the reasoning model selector for quickly finding models in large lists (e.g., Vercel AI Gateway with 200+ models)
• Show model ID alongside the display name on cards when they differ (useful for custom endpoints where IDs like meta-llama/llama-4-scout-17b-16e-instruct aren't obvious from the label)
• Support custom model IDs via the same input field — type any model ID and press Enter or click the checkmark to use it, even if it's not in the fetched list (e.g., gpt-4o on an Azure BYOK endpoint)
• Add vertical scrolling to the model list with a max height
• Two-line card layout: name + ID on first line, description below

Test plan

[x] Test custom model ID selection via Enter and checkmark button
[x] Verify custom endpoint with many models (e.g., https://ai-gateway.vercel.sh/v1) shows the filter input
[x] Verify local model picker is unaffected (no allowCustomModel passed)

Screenshot