> 50 is the hardware limit

this can't be true, If that hardware can run Django and Phoenix, it for sure can handle orders of magnitudes more concurrent clients than 50 even before you start tuning the OS and the runtime.

> Playwright headless Chromium

maybe you mean you're unable to generate more than 50 concurrent clients using Playwright+Chromium - but that's the wrong tool for loadtesting.

Loadtest should run from a different machine or cluster of machines/VMs. You can generate up to ~ 64K outgoing connections per IP address / alias. With 17 IP addresses/aliases you can generate up to C1M.