I'd skip the ternary and go with

foo = Optional.ofNullable(bar)
        .map(Bar::baz)
        .orElse(null);

But if I didn't, I'd use the first form.

In java 9 there is Objects.requireNonNullElse(obj, defaultValue)

If I had to go with the ternary operator, I would choose not to negate the statement for the sake of readability.

If I had free will of choice I would prefer using the Optionals API, like @MagicShel@programming.dev did.

The first one. Readability is quicker, and you don't have to stack context in your head if it's ==.

Personally though, I prefer what I call short circuiting. Return right away if it's null, basically input sanitization.

I think generally it’s preferably to work in the affirmative, i.e. bar == null? but I’ll admit I don’t stick to this 100% of the time and generally just use whatever feels better / more appropriate in the moment

I think the meat being more prominent in the second one is subjective. If I were writing a method to do something like this with ifs, I would handle the edge cases first and return early from them. The meat would be what's left after the edge cases. So this lines up with the first form.

I actually prefer

Optional.of(bar)
    .map(Bar::baz)
    .orElse(null)

You can crucify me but there is no way to miss the point in a quick glance here and I doubt that with JVM optimizations there is any meaningful performance impact, exceptionally in business code.

The second, or early return/continue/break.

But don't forget the third option:

foo = null
if (bar != null)
    foo = bar.baz();

This is much more readable if nontrivial; the only downside is that this inhibits the practice of ubiquitous final.

Actually, doesn't Java allow lazy final if you don't initialize (that would require explicit else)? I speak too many languages ...