Not sure why you're being downvoted. IIUC, pgvector uses a clustering implementation similar to ones implemented by FAISS. These are pretty simple / straightforward to implement but do not give the best performance. For more on the current SOTA, which are primarily graph-based algorithms like HNSW and Vamana I would check out https://big-ann-benchmarks.com/

I haven't actually used it yet, it can be very efficient to compute right next to where your data is though. A lot of inefficiency comes into play when you're marshalling data around between servers.

And you want to grab that fish out of the oven. In my opinion, the use case is not to install this on your OLTP database. You want this on some side server where you could apply change data capture.