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/app-server/tests/suite/v2/model_provider_capabilities_read.rs

@@ -57,7 +57,7 @@ async fn read_amazon_bedrock_provider_capabilities() -> Result<()> {
     let expected = ModelProviderCapabilitiesReadResponse {
         namespace_tools: true,
         image_generation: false,
-        web_search: false,
+        web_search: true,
     };
     assert_eq!(received, expected);
     Ok(())