fix: cache vars and remapping normalization

[devsergiy]

Use cache for variables normalization and variables remapping.

Closes ENG-8477

Summary by CodeRabbit

• Performance

  • Added dedicated caching for variable normalization and variable remapping to improve request processing and surface cache-hit visibility.
  • New debug headers report variable-normalization and variable-remapping HIT/MISS state for requests.

• Tests

  • Added tests covering normalization and remapping cache scenarios, including variable extraction, operation isolation, and list/value coercion; tests assert cache-hit headers and responses.