Comply with and verify HTML and JavaScript rendering to W3C standards, same as usual.
For instance, employ the W3C (or some other) markup validator: https://validator.w3.org/
Here are the common security mistakes: https://owasp.org/www-project-top-ten/
If you accept online payments, comply with the security requirements associated with those.
Implementing accessibility and privacy are among the areas that can involve some thought, too.
Most of the rest of this sort of consulting tends to be tailored to your plans, to your location and applicable regulations, and to your particular situation and budget. Those are not details that typically get discussed around here.
Closest cross-over here might be some WebKit rendering issue or such, and that might be better discussed with the WebKit developers via their bug-tracking system, for instance.
For what is new with Apple technologies, see the WebKit release notes. (I’d usually also hew closer to what is common and standardized too, rather than to tying the website specifically into the WebKit-based browsers.)