I work at Microsoft but at a completely unrelated team and while I know some of the folks who work on playwright I have no official affiliation and my opinions represent my own and not my employer's.
Playwright is great for this sort of thing! All we do is run the same test with two variants (before/after the change) and run a student t-test (well, a welch t-test but close enough).
It's ±50 LoC and as long as you're fine with running the test enough times to get statistical significance Playwright works quite well for this
If you want to get a sense of how far the system can scale, you would be better with a proper performance testing framework that can run multiple threads, ideally from multiple locations (to avoid any network limits) and built-in support for accurate timing. Apache Bench is pretty common and relatively easy to setup and use. There is also JMeter and even SaaS services to do it for you.
For most real-world performance tests, you should be adding plenty of delay. The average delay on the web between pages for real users runs around 50 seconds, last I looked (which was a while ago, admittedly).
If your app uses keepalives, or polling, or websockets, running your users really fast is going to make your test less accurate and you may get a false positive.