Pretty sure they’re hardcoded on my EE BR, but it’s been ages since I watched the actual disc (and I’m at work right now) so I can’t confirm.
The BluRays / DVDs for USA have burnt-in subtitles, and the BluRays / DVDs for Europe and other regions have player-generated subtitles. As easy as that.
With one noteable exception: at least the Middle-Earth Wooden Box BluRay versions (UK) have the same discs as the US versions, i.e. burnt-in. Don’t know how it was done on the older UK EiV editions.
Is the European BD of the theatrical version also soft subs? Or just the extended edition?
Yes.