You have to tell them. You are still technically an employee of theirs. ESP if you have their medical becuase you won’t be able to get the Medical through your other employer. They will put all the proper paperwork through. And if you have the pension with them you would need to give your leave if you want to take it with you (which I HIGHLY RECOMMEND as soon as you give your notice).
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I would recommend that you submit your resignation since you are still technically an employee. It might feel good to ghost them like they ghosted you but you may want a reference from someone you worked with some day. Or they might be in a position to influence an employment decision. Don’t burn your bridges.