agent: Improve error handling and retry for zed-provided models (#33565)

* Updates to `zed_llm_client-0.8.5` which adds support for `retry_after`
when anthropic provides it.

* Distinguishes upstream provider errors and rate limits from errors
that originate from zed's servers

* Moves `LanguageModelCompletionError::BadInputJson` to
`LanguageModelCompletionEvent::ToolUseJsonParseError`. While arguably
this is an error case, the logic in thread is cleaner with this move.
There is also precedent for inclusion of errors in the event type -
`CompletionRequestStatus::Failed` is how cloud errors arrive.

* Updates `PROVIDER_ID` / `PROVIDER_NAME` constants to use proper types
instead of `&str`, since they can be constructed in a const fashion.

* Removes use of `CLIENT_SUPPORTS_EXA_WEB_SEARCH_PROVIDER_HEADER_NAME`
as the server no longer reads this header and just defaults to that
behavior.

Release notes for this is covered by #33275

Release Notes:

- N/A

---------

Co-authored-by: Richard Feldman <oss@rtfeldman.com>
Co-authored-by: Richard <richard@zed.dev>

crates/web_search_providers/src/cloud.rs

@@ -7,10 +7,7 @@ use gpui::{App, AppContext, Context, Entity, Subscription, Task};
 use http_client::{HttpClient, Method};
 use language_model::{LlmApiToken, RefreshLlmTokenListener};
 use web_search::{WebSearchProvider, WebSearchProviderId};
-use zed_llm_client::{
-    CLIENT_SUPPORTS_EXA_WEB_SEARCH_PROVIDER_HEADER_NAME, EXPIRED_LLM_TOKEN_HEADER_NAME,
-    WebSearchBody, WebSearchResponse,
-};
+use zed_llm_client::{EXPIRED_LLM_TOKEN_HEADER_NAME, WebSearchBody, WebSearchResponse};
 
 pub struct CloudWebSearchProvider {
     state: Entity<State>,
@@ -92,7 +89,6 @@ async fn perform_web_search(
             .uri(http_client.build_zed_llm_url("/web_search", &[])?.as_ref())
             .header("Content-Type", "application/json")
             .header("Authorization", format!("Bearer {token}"))
-            .header(CLIENT_SUPPORTS_EXA_WEB_SEARCH_PROVIDER_HEADER_NAME, "true")
             .body(serde_json::to_string(&body)?.into())?;
         let mut response = http_client
             .send(request)