Hey! I'm a PM on the Azure PG team and work on AI features on Postgres. Wanted to address your points directly because we actually ship the capabilities you're asking about, we have made ALOT of progress in the last 3-6 months:
Hybrid search (BM25 + vector): Worth noting that ParadeDB's pg_search isn't an AWS-native feature either, you'd need to self-host it on EC2. On Azure PostgreSQL, we built pg_textsearch which provides the same BM25 ranking model (term frequency saturation, document-length normalization, IDF) natively. Fun fact, the main contributor of pg_textsearch is now on the Azure Postgres team :)
High-dimensional vectors: This is actually an area where we're ahead. pgvector with HNSW caps at 2,000 dimensions. We support pgvector for vector storage and search, and for high-dimensional / large-scale workloads we ship pg_diskann — Microsoft's graph-based vector index that supports up to 16,000 dimensions and also does advanced in-index filtering (your WHERE clauses get evaluated during graph traversal, so you don't lose recall on selective predicates).
These are available today on Azure PostgreSQL, specifically Azure HorizonDB (Preview). Happy to dig into specifics if you have a particular workload in mind.