perf(ttft): salvage easy-win startup optimizations from #3346 (#3395)

* perf(ttft): dedupe shared tool availability checks

* perf(ttft): short-circuit vision auto-resolution

* perf(ttft): make Claude Code version detection lazy

* perf(ttft): reuse loaded toolsets for skills prompt

---------

Co-authored-by: kshitijk4poor <82637225+kshitijk4poor@users.noreply.github.com>

run_agent.py

@@ -62,7 +62,12 @@ else:
 
 
 # Import our tool system
-from model_tools import get_tool_definitions, handle_function_call, check_toolset_requirements
+from model_tools import (
+    get_tool_definitions,
+    get_toolset_for_tool,
+    handle_function_call,
+    check_toolset_requirements,
+)
 from tools.terminal_tool import cleanup_vm
 from tools.interrupt import set_interrupt as _set_interrupt
 from tools.browser_tool import cleanup_browser
@@ -2520,7 +2525,13 @@ class AIAgent:
 
         has_skills_tools = any(name in self.valid_tool_names for name in ['skills_list', 'skill_view', 'skill_manage'])
         if has_skills_tools:
-            avail_toolsets = {ts for ts, avail in check_toolset_requirements().items() if avail}
+            avail_toolsets = {
+                toolset
+                for toolset in (
+                    get_toolset_for_tool(tool_name) for tool_name in self.valid_tool_names
+                )
+                if toolset
+            }
             skills_prompt = build_skills_system_prompt(
                 available_tools=self.valid_tool_names,
                 available_toolsets=avail_toolsets,