docs: document COYOTE_CURRENT_MODEL tool env and web_search_coyote current-model preference

Custom-Bash-Tools.md

@@ -37,6 +37,11 @@ A few things to know about how Coyote runs your tool's subprocess:
   environment variable (the environment variable takes precedence; default: `1800` seconds; `0` = unlimited). If the
   tool exceeds it, the process is killed and a `tool_call_error` is returned to the model, and the session keeps
   going. See [Environment Variables](Environment-Variables).
+* **`COYOTE_CURRENT_MODEL` identifies the session's active model.** Every tool subprocess (foreground tool calls and
+  `job__start` background jobs alike) receives the running session's model in `client:name` form (e.g.
+  `claude:claude-opus-5`). Tools can use it to adapt behavior to the model driving the session — the bundled
+  `web_search_coyote.sh` uses it to run native web search on the current model when supported. Read it defensively
+  (`"${COYOTE_CURRENT_MODEL:-}"`); agent-declared `variables:` envs with the same name take precedence.
 
 The following section explains how you can add parameters to your bash functions and how to test out your scripts.
 

Environment-Variables.md

@@ -61,6 +61,7 @@ The following environment variables are available for clients in Coyote:
 | `COYOTE_PATCH_{client}_CHAT_COMPLETIONS` | Patch chat completion requests to models on the corresponding client; Can modify the URL, body, <br>or headers.                                                                                                                                    | 
 | `COYOTE_SHELL`                           | Specify the shell that Coyote should be using when executing commands                                                                                                                                                                              |
 | `COYOTE_TOOL_TIMEOUT`                    | Wall-clock cap in seconds for any single tool-call subprocess (built-in and custom tools alike). <br>When exceeded, the tool process is killed and a `tool_call_error` is returned to the model instead of hanging the session forever. <br>Set to `0` for unlimited. Default: `1800` (30 minutes). <br>Counterpart of the `tool_timeout` config key; the environment variable takes precedence.                                        |
+| `COYOTE_CURRENT_MODEL`                   | Set **by** Coyote (not read by it) in the environment of every tool-call subprocess: the running session's active model in `client:name` form (e.g. `claude:claude-opus-5`). <br>Lets tools adapt to the model driving the session — e.g. `web_search_coyote.sh` prefers the current model for native web search when it supports it, falling back to `WEB_SEARCH_MODEL` otherwise. <br>Agent-declared `variables:` envs with the same name take precedence.                                        |
 
 # Files and Directory Related Variables
 You can also customize the files and directories that Coyote loads its configuration files from:

Graph-Agents.md

@@ -494,6 +494,7 @@ from normal agents:
 | `LLM_AGENT_VAR_<NAME>`          | One per declared `variables:` entry; uppercased name           |
 | `PATH`                          | Coyote's functions bin dir prepended to the inherited `PATH`   |
 | `CLICOLOR_FORCE`, `FORCE_COLOR` | Both set to `1` so child tools emit ANSI colors                |
+| `COYOTE_CURRENT_MODEL`          | The session's active model in `client:name` form               |
 
 The script's **working directory** is the coyote invocation directory (where
 the user ran `coyote -a <agent> ...`), not the agent directory. This matches

Tools.md

@@ -42,7 +42,7 @@ be enabled/disabled can be found in the [Configuration](#configuration) section
 | [`search_wolframalpha.sh`](https://github.com/Dark-Alex-17/coyote/blob/main/assets/functions/tools/search_wolframalpha.sh)     | Get an answer to a question using Wolfram Alpha. The input query should be <br>in English. Use it to answer user questions that require computation, detailed <br>facts, data analysis, or complex queries.                          | 🔴               |
 | [`send_mail.sh`](https://github.com/Dark-Alex-17/coyote/blob/main/assets/functions/tools/send_mail.sh)                         | Send an email.                                                                                                                                                                                                                       | 🔴               |
 | [`send_twilio.sh`](https://github.com/Dark-Alex-17/coyote/blob/main/assets/functions/tools/send_twilio.sh)                     | Send SMS or Twilio Messaging Channels messages using the Twilio API.                                                                                                                                                                 | 🔴               |
-| [`web_search_coyote.sh`](https://github.com/Dark-Alex-17/coyote/blob/main/assets/functions/tools/web_search_coyote.sh)         | Perform a web search to get up-to-date information or additional context. <br>Use this when you need current information or feel a search could provide <br>a better answer.                                                         | 🟢               |
+| [`web_search_coyote.sh`](https://github.com/Dark-Alex-17/coyote/blob/main/assets/functions/tools/web_search_coyote.sh)         | Perform a web search to get up-to-date information or additional context. <br>Use this when you need current information or feel a search could provide <br>a better answer. <br>Prefers the running session's model (`COYOTE_CURRENT_MODEL`) when it supports <br>native web search, falling back to `WEB_SEARCH_MODEL` (set `WEB_SEARCH_USE_CURRENT_MODEL=false` to always use the fallback).                                                         | 🟢               |
 | [`web_search_perplexity.sh`](https://github.com/Dark-Alex-17/coyote/blob/main/assets/functions/tools/web_search_perplexity.sh) | Perform a web search using the Perplexity API to get up-to-date <br>information or additional context. Use this when you need current <br>information or feel a search could provide a better answer.                                | 🔴               |
 | [`web_search_tavily.sh`](https://github.com/Dark-Alex-17/coyote/blob/main/assets/functions/tools/web_search_tavily.sh)         | Perform a web search using the Tavily API to get up-to-date <br>information or additional context. Use this when you need current <br>information or feel a search could provide a better answer.                                    | 🔴               |