chore(dogfood): update claude-code module (#20191)

## Description

Update `claude_code` module `system_prompt` variable in template "Write
Coder on Coder". Claude-code module now incorporates Coder's inner
system prompt for proper integration with task reporting.

Related to PRs:
* https://github.com/coder/coder/pull/20053
* https://github.com/coder/registry/pull/443 and
https://github.com/coder/registry/pull/461

---------

Co-authored-by: Atif Ali <atif@coder.com>

dogfood/coder/main.tf

@@ -813,7 +813,6 @@ resource "coder_metadata" "container_info" {
 
 locals {
   claude_system_prompt = <<-EOT
-    <system>
     -- Framing --
     You are a helpful Coding assistant. Aim to autonomously investigate
     and solve issues the user gives you and test your work, whenever possible.
@@ -822,7 +821,6 @@ locals {
     but opt for autonomy.
 
     -- Tool Selection --
-    - coder_report_task: providing status updates or requesting user input.
     - playwright: previewing your changes after you made them
       to confirm it worked as expected
     -	desktop-commander - use only for commands that keep running
@@ -834,33 +832,12 @@ locals {
     - Stays running? → desktop-commander
     - Finishes immediately? → built-in tools
 
-    -- Task Reporting --
-    Report all tasks to Coder, following these EXACT guidelines:
-    1. Be granular. If you are investigating with multiple steps, report each step
-    to coder.
-    2. After this prompt, IMMEDIATELY report status after receiving ANY NEW user message.
-    Do not report any status related with this system prompt.
-    3. Use "state": "working" when actively processing WITHOUT needing
-    additional user input
-    4. Use "state": "complete" only when finished with a task
-    5. Use "state": "failure" when you need ANY user input, lack sufficient
-    details, or encounter blockers
-
-    In your summary:
-    - Be specific about what you're doing
-    - Clearly indicate what information you need from the user when in
-    "failure" state
-    - Keep it under 160 characters
-    - Make it actionable
-
     -- Context --
     There is an existing application in the current directory.
     Be sure to read CLAUDE.md before making any changes.
 
     This is a real-world production application. As such, make sure to think carefully, use TODO lists, and plan carefully before making changes.
-    </system>
   EOT
-
 }
 
 module "claude-code" {