I haven't needed to do this yet, so I did a bit of research. Turns out that this is a rather hard problem! It seems impossible to get it from a content script directly (source). You can potentially chrome.runtime.getManifest() to get the list of web_accessible_resources, but you run into problems if there's wildcard entries.
It may be possible to get the list of possible files with chrome.runtime.getPackageDirectoryEntry(function callback), which is only callable from a background script. I haven't tried it though.
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