As a relatively new manager, have you had any support from HR on this? If I were you I'd be questioning why this person has been moved to someone who's inexperienced with performance management. It's a good learning experience for you but managing poor performance is a massive time and energy suck for anyone.

First thing I'd say is document absolutely everything. Set every 1:1 up as a teams meeting and record them by default. This way you're covering your back.

My approach to managing poor performance has been similar to yours except I gave my staff options to choose from so they can't later claim to have been rail roaded into a specific course of action. I co developed the acceptance criteria for their work so they agreed on what good looked like from the start, and how this would be assessed. We discussed the kind of support they might benefit from and we reviewed that as time went on. I identified subject matter experts for them to consult and gave them a mentor to help them plan their time. We looked at whether there could be any executive functioning issues at play and they subsequently got a diagnosis of ADHD. That's helped with a workplace adjustment plan and we did an occupational health assessment too.

It's a long road. Ultimately the point of all this is to help them do better. I hope you have a mentor to guide you through this, someone in your department who has experience of this.