That said, I suspect that you can probably beat SQS for a number of use cases, and definitely if you want to hold onto the data long term or search over it then S3 has huge options there.
Performance will be extremely solid unless you need your worst case latency for "push -> pop" to be very tight in your p90.
If you want consistently really low latency/ can't tolerate a 50ms spike, don't retain tons of data, have <10K/s writes, and need complex indexing that might change over time, Postgres is probably what you want (or some other thing). If you know how your data should be indexed ahead of time, you need to store a massive amount, you care more about throughput than a latency spike here or there, or really a bunch of other use cases probably, S3 is just an insanely powerful primitive.
Insane storage also unlocks new capabilities. Immutable logs unlock "time travel" where you can ask questions like "what did the system look like at this point?" since no information is lost (unless you want to lose it, up to you).
Everything about a system like this comes down to reducing the cost of a GET. Bloom filters are your best friend, metadata is your best friend, prefetching is a reluctant friend, etc.
I'm not sure what I'm building. I had this idea years ago before S3 CAS was a thing and I was building a graph database on S3 with the fundamental primitive being an immutable event log (at the time using CRDTs for merge semantics, but I've abandoned that for now) and then maintaining an external index in Scylla with S3 Select for projections. Years later, I have fun poking at it sometimes and redesigning it. S3 CAS unlocked a lot of ways to completely move the system to S3.