In practice people seem to have adopted the various xorshift style generators - certainly IIRC from back when I worked on JSC (and so also paid attention to other JS engines) we all adopted xorshift128+ for all unsafe RNGs (Math.random, but also internal entropy used in mitigations and similar), though the general family is "xorshift"[1]. There are a few others, and for me this was a decade+ ago so maybe there have been improvements since - xorshift does fail some of the diehard tests but so few as to be acceptable for the overwhelming majority of cases.
There days I believe that the PCG RNG[2] family might be a better choice? They claim to be both faster and statistically better, but I'm guessing not by enough for JS engines to care (RNG performance was a 10-20 years ago as the increasing perf of the rest of the engines meant the cost of Math.random() in benchmarks started being a problem lol - JSC at the time used two calls to the system arc4random(), which required call overhead and the system implementation required locking, but it was cryptographically secure! at least on Mac+iOS where it is not actually RC4).
Very very big NB: If you're wanting random numbers to feed into _any_ part of _anything_ cryptographic (keys, nonces, padding, ...) use the OS provided secure RNG, do not try and do it yourself - not just because of "it's real easy to get it wrong", but because the system APIs automatically leverage hardware RNGs automatically when possible (the semi-mythical "true random").
[1] https://en.wikipedia.org/wiki/Xorshift [2] https://www.pcg-random.org/index.html
Just a page with SmallCrush and BigCrush examples, not to be taken as an endorsement for their PRNG: https://www.pcg-random.org/statistical-tests.html
It's pretty straightforward and builds off basic primitives, but the results has some neat qualities/features if you find you need them. E.g. People often find that they don't want pure randomness, but rather want some kind of uniformity//equidistribution over some period, which implies state (I.e. Shuffling a music playlist).