I'm not sure if it'll be dealt with much differently with COVID, but here's a rough idea of what to expect: If you've had issues with depression in the past, you'll probably be referred to a psychiatrist who will discuss your history and write a report back to the AME based on this. It won't be anything to worry about; just a chat to understand how it came about and make sure you are well now.
The AME will send this off to the CAA and you'll be invited for a chat with their psychiatrist who will review the notes with you and again make sure you are well now. All being well you should then get your medical in the post shortly afterwards. I hope that helps!