From my understanding, the Crown's role is largely symbolic in UK in reality.
Is the monarch privy to any UK state secrets that normal non-government civilians wouldn't be privy to? Does the Queen get automatic security clearance?
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There has been public confirmation that the Queen (and also Prince Charles) is on the standard circulation list for Cabinet memoranda. More directly, information about things like security arrangements for the royal family are obviously not for public consumption.
If you've not watched the Netflix series The Crown, I highly suggest you do so. Of particular note is the Red Box that the Queen gets almost every day
These boxes contain Cabinet and Foreign and Commonwealth Office documents, most of which the monarch must sign and give Royal Assent to, before they can become law.
Remember, the Queen is literally the UK government. So a better question here isn't
What secrets is she privy to?
Is there anything that cannot be disclosed to the Queen?
As the government of the UK, the answer seems to be "No". That having been said, I'm not sure they necessarily give her a briefing of every state secret either.