OK, turns out that the issue was:

"awslogs-datetime-format": "%Y-%m-%d %H:%M:%S"

In the ECS task definition log configuration. Since the granularity was set to seconds, every request that occurred in "the same second" would have its log grouped under one entry by the awslogs driver.
https://docs.aws.amazon.com/batch/latest/userguide/using_awslogs.html
This behavior is hinted in the official AWS documentation, although imho it's not stated clearly enough.