Generally speaking, you wouldn't want to run queries like this against the system of record (your database) in large applications where there are a lot of user

Generally speaking, you wouldn't want to run queries like this against the system of record (your database) in large applications where there are a lot of user queries, as that will impact performance. Hence why solutions like elasticsearch and apache solr exist. They scale very well horizontally, allowing you to spread the load between multiple nodes. Again, this comes down to what your use case is. If you have a tiny app with a relatively small number of users, using postgres for this functionality is probably ok.