Like the photos Tarev...Jelinda, I would do what you said plant it in a bit larger pot but keeping the roots as untouched as possible. And only water lightly
I found that with succulents especially babies, I could water once per week but very lightly (I'd been used to other house plants watering once per week until the water runs through, or soaking in the sink) succulents as you know wouldn't want that in the winter
Cheers