Fm/debug examples

[filip-michalsky]

Description

Two fixes for the BrowserEnv CUA mode and a DX improvement for the DOM example:

1. Fix screenshot passing in CUA messages: Screenshots attached as image_url parts inside tool messages were being dropped by clients. The new env_response override in
   BrowserEnv relocates image_url parts out of tool messages into a trailing UserMessage so they are preserved. Also normalizes empty tool-call arguments to "{}" to prevent
   json.loads("") decode failures on zero-arg tools (e.g. screenshot).

2. Make filter_screenshots_in_messages robust to mixed content types: Content parts can be plain dicts or Pydantic objects. Updated type checks in CUAMode to handle both
   via _get_item_type() helper and getattr fallback.

3. DX improvement for DOM example: Made project_id optional in load_environment() — it now falls back to the BROWSERBASE_PROJECT_ID env var at runtime. Removed the
   upfront env-var validation that eagerly errored before the environment was even used.

Type of Change

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Documentation update
• Test improvement

Testing

• All existing tests pass when running uv run pytest locally.
• New tests have been added to cover the changes

Checklist

• My code follows the style guidelines of this project as outlined in AGENTS.md
• I have performed a self-review of my own code
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• Any dependent changes have been merged and published

Additional Notes

Files changed:

• environments/browser_dom_example/browser_dom_example.py — make project_id optional, remove eager env-var check
• verifiers/envs/integrations/browser_env/browser_env.py — new env_response override: sanitize empty tool args + relocate screenshots from tool messages to user messages
• verifiers/envs/integrations/browser_env/modes/cua_mode.py — handle dict and Pydantic content parts in filter_screenshots_in_messages

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Note

Medium Risk
Touches BrowserEnv.env_response message post-processing in CUA mode, which can affect how tool outputs and multimodal context are presented to models; changes are targeted and covered by new tests but impact core browser-agent I/O.

Overview
Fixes CUA-mode message post-processing so screenshots and tool calls survive provider/adaptor quirks. BrowserEnv.env_response now (1) normalizes empty tool_call.arguments to {} for zero-arg tools and (2) extracts image_url parts from ToolMessage content and appends them as a trailing UserMessage, leaving non-image tool content intact.

Hardens screenshot filtering and improves example DX. CUAMode.filter_screenshots_in_messages now handles content parts that are dicts or Pydantic objects, and the DOM example’s load_environment() makes project_id optional while removing eager env-var validation. New tests cover the CUA env_response relocation behavior and the no-images case.

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