[Skills] Apply code standards skill (#35459)
### Details:
This PR adds a skill that automates detection and remediation of all
code standard violations introduced by a branch's changes in the C++
codebase.
The skill covers three categories in order:
1. Copyright headers — checks via check_copyright.py, auto-fixes by
inspecting and applying the generated patch, falls back to manual edit
if the patch looks wrong.
2. clang-tidy / compilation — builds affected CMake targets with
`ENABLE_CLANG_TIDY=ON`. Separates plain compilation errors (fixed
manually) from clang-tidy diagnostics (auto-fixed via
`ENABLE_CLANG_TIDY_FIX=ON`, then manual fallback). Compilation errors
are resolved first since tidy cannot auto-fix a file that doesn't
compile.
3. clang-format — runs `clang_format_check_all`, auto-fixes with
`clang_format_fix_all`, re-verifies.
### Tickets:
- *N\A*
### AI Assistance:
- *AI assistance used: yes*
- *AI was used for skill testing and improvement: generating test cases,
running the skill, adjust the instructions based on user's feedback and
test results*
