Enable cached web search for Amazon Bedrock (#36938)

## Why

Amazon Bedrock supports hosted text web search, but it rejects the
`search_content_types` field used for multimodal search and does not support
external live or indexed web access.

## What changed

- Advertise hosted web search for Amazon Bedrock while marking external web
  access as unsupported.
- Resolve unsupported live and indexed modes to cached search, or disable the
  tool when cached search is prohibited by managed requirements.
- Normalize built-in and configured Bedrock model catalogs to text-only web
  search, and retain the runtime provider in session configuration so turn
  setup can apply its capabilities.

## Testing

- Cover cached fallback, managed-mode restrictions, text-only tool payloads,
  provider capabilities, and catalog normalization.

GitOrigin-RevId: 310473849257401654388a4ebb42920e03aa3228

codex-rs/model-provider/src/provider.rs

@@ -35,6 +35,7 @@ pub struct ProviderCapabilities {
     pub namespace_tools: bool,
     pub image_generation: bool,
     pub web_search: bool,
+    pub external_web_access: bool,
 }
 
 impl Default for ProviderCapabilities {
@@ -43,6 +44,7 @@ impl Default for ProviderCapabilities {
             namespace_tools: true,
             image_generation: true,
             web_search: true,
+            external_web_access: true,
         }
     }
 }