Does PDF Extract API support hyperlink extraction?

Yes. It supports hyperlink extraction. Try the attached file. You'll see the hyperlinks on the right that are represented like this...

{
    "Bounds": [
        427.7200012207031,
        355.3280029296875,
        524.5761413574219,
        377.3710021972656
    ],
    "Font": {
        "alt_family_name": "Clean",
        "embedded": true,
        "encoding": "Custom",
        "family_name": "Adobe Clean",
        "font_type": "Type1",
        "italic": false,
        "monospaced": false,
        "name": "FHQAMC+AdobeClean-Bold",
        "subset": true,
        "weight": 700
    },
    "HasClip": false,
    "Lang": "en",
    "Page": 0,
    "Path": "//Document/Aside/P[2]/Reference",
    "Text": "(<https://www.adobe.io/apis/documentcloud/dcsdk/>)Adobe Acrobat Services › (<https://www.adobe.io/apis/documentcloud/dcsdk/pdf-extract.html>)Adobe PDF Extract API › ",
    "TextSize": 9,
    "attributes": {
        "LineHeight": 11
    },
    "elementId": 15
},