It is currently not possible to access objects embedded in <object> tags:

<object data="file.svg" type="image/svg+xml"></object>
<object data="file.html" type="text/html"></object>
<object data="file.xhtml" type="application/xml+xhtml"></object>

First, none of the locator strategies are able to "deep-select" elements originating from objectElement.contentDocument.

Second, bypassing the selection problem by executing a custom JS script in order to return the nested elements results in "stale element reference" error upon usage of the acquired reference. This could be solved if a switch to an object's contentDocument context was possible.

My use case in my application for embedding an SVG via <object> is that I can quickly replace it by setting the data URI while maintaining access to its contents via contentDocument.