Extensions are banned entirely in $lookup but support will be added behind featureFlagExtensionsInsideHybridSearch in a concurrent project (see Technical Design: Refactor rankFusion/scoreFusion to support extension stages). In DocumentSourceExtensionOptimizable::create():

static boost::intrusive_ptr<DocumentSourceExtensionOptimizable> create(...) {
    if (expCtx->getInLookup() && !feature_flags::featureFlagExtensionsInsideHybridSearch.isEnabled()) {
        throwIfrKickbackIfNecessary(name, isExtensionSearchStage, gFeatureFlagSearchExtension,search_metrics::inLookupKickbackRetries, "...");     
    }
    // ...
}

Integration Tests:

• $search/$searchMeta in $lookup with the appropriate flag disabled.
  • IFR kickback fires and the query retries.
  • The appropriate metric is incremented.
• $search/$searchMeta in $lookup with the appropriate flag enabled.
  • No IFR kickback or metric increment.