Aurora Max Connections

There's a few concerns when changing the default number of maximum connections, which is based on DB instance memory. More connections lead to more threads, and MySQL (and thus Aurora) doesn't have great workload management, so no thread prioritization, limits on resource consumption, etc. This all can increase resource contention. Memory management is also difficult, there are connection level buffers/caches and controlling their memory footprint is non-deterministic (it depends on sessions and active queries). This can be problematic because you can run out of memory if there's a lot of variability in these memory consumers, and the only way to limit that risk is by reducing the more predictable global memory consumers, such as the page cache/buffer pool, which are easier to control. That in turn can have detrimental performance implications.

While there's no set guidance on when to change the max connections value, stability of resource utilization and predictability of query patterns is something that is key. For example, a workload that only performs simple key/value lookups and updates with not a lot of variability in query patterns would be a better candidate for increasing max connections, then a workload with variable queries, complex aggregations, joins, and multi step transactions.

Ultimately, if you have to change that value, consider making small incremental changes, monitor freeable memory to make sure it's stable, and monitor lock contention between queries.