「僕達はあなたがどれほど頑張っているか心配です」
I know that 「か」in the middle of a sentence can be used for embedded questions or as "or," but I don't see any of that here.
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The embedded "question" in this case isn't really a question, but it is there
「あなたがどれほど頑張っているか」
is the English equivalent of
How hard you're working
For a very direct translation that comes out to something like
I'm worried about how hard you're working
Though it's worth noting that while the English sounds like something you would say to someone who you were worried was working too hard, the above Japanese sounds to me like it means the opposite. Of course it's very difficult to be certain without context.
Use of どれぐらい/どう/どれほど/etc. + か in subordinate clauses to talk about the degree or manner of something is very common, the same way how is used in subordinate clauses in English. Here's another example from an online dictionary:
自分がどう思われているのか心配する
Worry about how one is being perceived
思われてる of course literally means "thought of" for "how one is being thought of". "Perceived" is just more natural English.
