Hello
No, Piwigo has an fully featured Api

how would you use Oembed? in which context?

Wordpress only allows some website to be rendered as oEmbed
PiwigoPress is what you need

Oembed would do as mush as PiwigoPress which is displaying a thumbnail as a link to the gallery picture/album page

if you want the whole gallery inside wordpress... that's pointless ; you can use an iframe but that's against accessibility for mobile and disabled people. Just customize both theme to be similar