[html] Multiple "style" attributes in a "span" tag: what's supposed to happen?

In HTML, SGML and XML, ⁽¹⁾ attributes cannot be repeated, and should only be defined in an element once.

So your example:

<span style="color:blue" style="font-style:italic">Test</span>

is non-conformant to the HTML standard, and will result in undefined behaviour, which explains why different browsers are rendering it differently.

Since there is no defined way to interpret this, browsers can interpret it however they want and merge them, or ignore them as they wish.

^{(1): Every article I can find states that attributes are "key/value" pairs or "attribute-value" pairs, heavily implying the keys must be unique. The best source I can find states:}

^{Attribute names (id and status in this example) are subject to the same restrictions as other names in XML; they need not be unique across the whole DTD, however, but only within the list of attributes for a given element. (Emphasis mine.)}