While this is more a case-by-case question (as many extensions have special dependencies), I am trying to offer some background information for you reference.

Why an extension needs separate downloads

Many reasons but typical ones are,

• Make the main downloads from VS Code Marketplace small
• Host OS dependent dependencies (language server/debugger or others) externally so that at runtime the extension downloads only for a specific OS.

Many extensions can utilize the new platform specific packaging mode of vsce, but not for old extensions out of maintenance.

Is there a common way for extension authors to specify such separate downloads?

No. VS Code does not have a standard here, so extension authors can do whatever they like.

Tabnine specific

Now back to your question. To learn what tabnine extension wants to download and where on disk those files should be put, your only option is to ask its developer(s) or dig into the source code.

Side Notes

I did internalize many similar extensions for my clients under the product Scarborough for VS Code, so I would like to kindly inform you that many extensions were never designed to work in an environment without internet access. So you might need more hacking than you initially thought.