"I am happy to notice that you are doing way better."
Translation:Je suis content de constater que tu vas beaucoup mieux.
In absolute terms, I agree, but I'd like to add a precision:
- In this sentence, it does not really make sense to use the verb "faire", since "you are doing better" refers to the idiomatic phrase that usually translates to "tu vas mieux" or "vous allez mieux".
- That is why "tu fais mieux" and "vous faites mieux" are not accepted here.
s'apercevoir is reflexive and its meaning is quite different
"je suis heureux de voir/constater que tu vas mieux" are the most natural verbs. Their meanings are neutral, just about an objective perception.
"je m'aperçois que je n'ai pas mes clés": (Suddenly) I realize/find out that I don't have my keys