fix(skills): Make SkillToolset system instruction respect tool_filter

[nicobytes]

Summary

• Build the skill system instruction from tools actually selected by tool_filter (list or predicate)
• Stop advertising run_skill_script / load_skill_resource when filtered out, and explicitly tell the model not to call them — reply as normal text instead
• Also keep the rest of process_llm_request consistent with the filter: inject skills XML when list_skills is filtered out, and omit the search_skills registry hint when that tool is filtered out
• Leave tool registration unchanged (related follow-up: SkillToolset exposes run_skill_script tool causing hallucination loop when skill has no scripts/ directory #6281)

Why

get_tools() already respected tool_filter, but process_llm_request always injected _build_skill_system_instruction(), which unconditionally told the model to use run_skill_script and load_skill_resource. With instruction-only skills (tool_filter=["list_skills", "load_skill"]), Gemini often wrapped the final reply in a hallucinated run_skill_script call → UNEXPECTED_TOOL_CALL / ValueError: Tool 'run_skill_script' not found. and an empty user-facing response.

Fixes #6448
Related to #6281

Testing Plan

• Unit: filtered instruction omits positive usage of script/resource tools and adds an explicit ban
• Unit: unfiltered DEFAULT_SKILL_SYSTEM_INSTRUCTION contract unchanged
• Unit: process_llm_request with tool_filter=["list_skills", "load_skill"] injects filtered instruction
• Unit: excluding list_skills injects skills XML fallback
• Unit: registry + filter excluding/including search_skills controls the registry hint
• Unit: tool_name_prefix + filter uses prefixed names in instruction/ban
• Unit: ToolPredicate filter is respected by the injected instruction
• Existing test_skill_toolset.py suite green

uv run pytest ./tests/unittests/tools/test_skill_toolset.py -q
# 123 passed

uv run pre-commit run --files src/google/adk/tools/skill_toolset.py tests/unittests/tools/test_skill_toolset.py
# all hooks Passed

Manual repro (pre-fix)

from google.adk import Agent
from google.adk.skills import models
from google.adk.tools.skill_toolset import SkillToolset

skill = models.Skill(
    frontmatter=models.Frontmatter(
        name="whatsapp-formatting",
        description="Format messages for WhatsApp native rendering.",
    ),
    instructions="Use *bold* and _italic_ WhatsApp syntax. No scripts.",
)

toolset = SkillToolset(
    skills=[skill],
    tool_filter=["list_skills", "load_skill"],
)

agent = Agent(
    model="gemini-flash-latest",
    name="demo",
    instruction="Help the user. Load the formatting skill when needed, then reply as text.",
    tools=[toolset],
)

Before: model often calls run_skill_script after load_skill → crash.
After: instruction no longer advertises filtered tools and tells the model to answer as normal text.

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[nicobytes]

recheck

[rohityan]

Hi @nicobytes , Thank you for your contribution! We appreciate you taking the time to submit this pull request. Your PR has been received by the team and is currently under review. We will provide feedback as soon as we have an update to share.

[rohityan]

Hi @sasha-gitg , can you please review this. LGTM