Have you actually had a 1:1 conversation with them to ask them how they feel about the situation? I've been through this twice, as the "failing" employee and when my DS was the "failing" employee.
In both cases HR/higher management etc were happy and the bullying boss was "following procedures", but also in both cases there hadn't actually been an initial conversation of "how do you think you are doing/do you need any help", before they jumped in with the meeting to say "you're shit and we are taking action".
I know you've said you've been supporting them and training, but my boss was adamant I'd had loads of training while I had no clue I was doing anything wrong. The bombardment of emails is also really soul destroying.
For example, mine would set me a task like: come up with a spreadsheet to record xyz. No specifics at all, no instructions. I had zero experience, which they didn't take into account. I would come up with the spreadsheet. It would be "wrong". She would completely redo it, huffing and sighing all the way, but never ever explain what she wanted or why it was wrong. She was always far too busy to sit with me and show me how she wanted something done.
One incident she asked me to save this document and keep it updated, which I did. She sent a link to the rest of the team having saved a different copy somewhere else. So of course I was updating the original, but everyone else was looking at her duplicate. It didn't come up until the end of year report, when she wrote "duplicate documents caused confusion". It wasn't my doing, yet she refused to accept responsibility!!
She absolutely refused to communicate except by email, even though we sat back to back and in my previous jobs we'd been encouraged to always speak F2F. So of course she had tons of email evidence of my wrongdoing, while I didn't because all mine had been to her face.
I am still really bitter about this as it held my progression back by 3 years, almost drove me to a breakdown, and cost me a lot of lost pay and bonuses, yet it was almost 10 years ago. I've had decent bosses since and the situation has never been repeated (except for my DS who got sacked).
Can you hand on heart say it's all the fault of this employee and you have done everything right? If they believe you are bullying them have you actually listened to what they are saying? Of course it's possible that they are as useless as you say and are being awkward, but there are 2 sides to every story. Perhaps get somebody neutral to mentor them, start from scratch and get to the bottom of it.