Since the Bible wasn't written in English, it was only translated into English, I'm not sure we can genuinely call anything Biblical English.
I don't have time right now to look into what type of English used "thou shalt" but Wikipedia gives a good history of the Bible's various translations into English here. By looking at the dates and comparing them with the dates that different versions of English were being used, it should be possible to work it out.
Even native speakers might not realise they're using an old form of English sometimes. If you asked a standard Brit to tell you what "You will" is in an ancient English form, they would probably say "I have no idea!" But you can bet your boots that if you asked them to give you an example of one of the ten commandments in an old style of English, they would say "Thou shalt not kill" or similar. It's funny how we don't realise we're using another language sometimes when it's part of a well-known phrase or saying.
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