Sure, PostgreSQL can be used for sessions, but Redis has solved this problem on virtually every single platform a long time ago. Your customer probably doesn't even know what a session is, but they will definitely learn about them when your in-house implementation inevitably encounters an edge case.
Of course, PostreSQL has wonderful search capabilities but it was never intended to be used as a search engine. Solr was created in 2004 and is still being improved and used in production every day. Do you know what will happen to your full-text search when your customer types in a mix of English and Chinese characters?
Yes, PostgreSQL addition of SKIP LOCKED was neat but AFAIK the author of that feature himself recommended using a traditional job queue unless you had a very good reason against it. RabbitMQ was designed as a message queue and when you read the documentation you realize that they had encountered virtually every single problem and figured out a way to deal with it so that you don't have to. The documentation pretty much tells you what problems you are going to have later so that you can plan for them today.
Choose boring technology (tm), follow industry best practices, and enable your team to get their work done using the right tools for the job, so they can deliver the product to the customer, and leave the office on time.