Overview

The extension test suites are moving to one suite family per feature-flag configuration (each all-flags-on except the named one; see SERVER-130636 for the hybridSearch_disabled family and SERVER-130878 for search_disabled). The original with_mongot_extension_* suites (only the $vectorSearch extension enabled) match none of the target configurations, so this ticket renames them into the vectorSearch_disabled family and updates their flag configuration to match its semantics.

Work

• Rename the 4 with_mongot_extension_ mappings/generated suites/Evergreen tasks/burn_in entries to with_mongot_extension_vectorSearch_disabled_.
• Flag config becomes: featureFlagVectorSearchExtension: false, featureFlagSearchExtension: true, featureFlagExtensionsInsideHybridSearch: true ($vectorSearch uses the server's legacy implementation; $search and hybrid search run through the Extensions API).
• Exclusions: shared exclude_incompatible_tests base + the exclude_search_extension_incompatible block (SERVER-131304/131305/131306). The extension-$vectorSearch-specific exclusions do not apply since $vectorSearch runs the legacy path.
• Triage new failures via an Evergreen patch on the extensions-secure variants: legacy $vectorSearch alongside extension $search + extension hybrid search is a previously untested combination.

Dependencies

Stacked on SERVER-130636 and SERVER-130878 (the override-block structure and the other families land there). The fully_enabled family (separate ticket) stacks on top of this one.