Well... we have 3 node MongoDB cluster and are processing up to a million trades... per second. And a trade is way more complex than a chat message. Has tens to hundreds of fields, may require enriching with data from multiple external services and then requires to be stored, be searchable with unknown, arbitrary bitemporal queries and may need multiple downstream systems to be notified depending on a lot of factors when it is modified.
All this happens on the aforementioned MongoDB cluster and just two server nodes. And the two server nodes are really only for redundancy, a single node easily fits the load.
What I want to say is:
-- processing a hundred million simple transactions per day is nothing difficult on modern hardware.
-- modern servers have stupendous potential to process transactions which is 99.99% wasted by "modern" application stacks,
-- if you are willing to spend a little bit of learning effort, it is easily possible to run millions of non trivial transactions per second on a single server,
-- most databases (even as bad as MongoDB is) have a potential to handle much more load than people think they can. You just need to kind of understand how it works and what its strengths are and play into rather than against them.
And if you think we are running Rust on bare metal and some super large servers -- you would be wrong. It is a normal Java reactive application running on OpenJDK on an 8 core server with couple hundred GB of memory. And the last time I needed to look at the profiler was about a year ago.