It's worth noting that Oracle has solved this problem. It has horizontal multi-master scalability (not sharded) and a queue subsystem called TxEQ which scales like Kafka does, but it's also got the features of a normal MQ broker. You can dequeue a message into a transaction, update tables in that same transaction, then commit to remove the message from the queue permanently. You can dequeue by predicate, delay messages, use producer/consumer patterns etc. It's quite flexible. The queues can be accessed via SQL stored procs, or client driver APIs, or it implements a Kafka compatible API now too I think.

If you rent a cloud DB then it can scale elastically which can make this cheaper than Postgres, believe it or not. Cloud databases are sold at the price the market will bear not the cost of inputs+margin, so you can end up paying for Postgres as much as you would for an Oracle DB whilst getting far fewer features and less scalability.

Source: recently joined the DB team at Oracle, was surprised to learn how much it can do.