I have a feeling that the page referenced is not so "modern" :-)
BUT, that doesn't make it a necessarily bad protocol for modern browsers to be implementing, i.e. as part of their "identity management" stuff, like Firefox Sync [1].
Remember that the Stanford Java applet implementation was purely academic, intended as a demonstration and developed at a time where JavaScript was too limited for the large number arithmetic they wanted to do (no BigInteger equivalent).
That purely academic implementation does not invalidate the work itself, or future implementations thereof.
[1] https://wiki.mozilla.org/Identity/AttachedServices/KeyServer...
Also it has the ability to generate a session key.
The good news is that using SRP is definitely not worse than DH as a key agreement protocol.
The bad news is you probably already have a nice modern ECDH key agreement protocol, you wanted secure passwords and the proof for how SRP does that involves a lot of flailing about. Flailing about which so far reached SRP version 6a
If browsers and backend stacks and everything else was one config change from doing SRP 6a tomorrow it's tempting to say hey, go ahead it can't hurt.
But in fact SRP is very niche, so it makes at least as much sense to try to deploy OPAQUE or other things that have a clearer security rationale.
On any client where you can run code you can authenticate without ever sending your plaintext password over the wire. And on clients where you can't run code you can still accept the plaintext password as a fallback.
There's nothing modern about a system that requires Java in the browser. No thanks.