Investigate reducing test recording size for functional tests

## Context

From PR #7672 review feedback by @wbreza:

The functional test recordings (YAML files in `test/functional/testdata/recordings/`) can be very large. For example, the AI quota preflight tests produce recordings with ~607KB per request for the CognitiveServices model catalog response, which includes costs, SKU variants, capabilities, deprecation timelines, and rate limits — none of which the test logic actually inspects.

The 3 RG-scoped recordings in #7672 are nearly identical (~1.56MB each / 5,206 lines) because they hit the same API responses with only minor parameter differences.

## Proposal

Investigate reducing recording size across all functional tests:

- **Strip responses** to only include fields the test logic reads
- **Share common base recordings** and parameterize differences
- **Compress or deduplicate** large API responses in the recorder

This would reduce PR footprint and CI artifact sizes for all functional tests, not just the quota check tests.

## Related

- PR #7672 — feat: add AI model quota preflight validation check