Reading this like “yep, yep, tried that… yep.” I’ve set expectations, had the tough conversations, even adjusted the role to better fit their strengths. Still no progress. At what point does patience turn into enabling? Have you ever let someone go and immediately felt relief? Because I’m getting close. https://www.fastcompany.com/91302949/how-to-know-when-to-coach-or-cut-a-struggling-employee
Have you sent them on training? Or asking if they actually want to be in this role? Or asking them if they are struggling with something specific in the role?
Sounds like you're there. Follow the company policy and engage HR.
Document everything.
Move on.
Purple are worried about the person leaving and yes they are impacted. But the mental grind and stress for you as their manager is long term and more impactful to your health and career.
I never want to get to USA level but if you've tried and it's not working cut them loose before you turn into a basket case.
Also to quote" noting demotivates a good employee than watching a bag one being tolerated" . If there are other people dealing with them talk to them. Ask them if they think anyone around is struggling. You could be surprised at how it's affecting their morale.
The damage someone who doesn't keep up does is difficult to keep in mind but important to you as a manager.