People screw up the bcrypt thing all the time. Pick a single threaded server stack (and run on one core, because Kubernetes), then configure bcrypt so brute forcing 8 character passwords is slow on an A100. Configure kubernetes to run on a medium range CPU because you have no load. Finally, leave your cloud provider's HTTP proxy's timeout set to default.
The result is 100% of auth requests timeout once the login queue depth gets above a hundred or so. At that point, the users retry their login attempts, so you need to scale out fast. If you haven't tested scale out, then it's time to implement a bcrypt thread pool, or reimplement your application.
But at least the architecture I described "scales".