Recently, I started sending cold mails to profs for upcoming PhD applications. Two of them replied instantly right after my mail:
Thank you for contacting me, I am planning taking graduate students and I have these two xx and yy projects fits your background very well. I strongly encourage you to apply our program and you can write my name as your choice of PI.
I definetly know that doesn't mean I am already accepted or anything, but at least really encouraged me since now I feel like I have a better chance for admission than I thought at the beginning.
Problem is, they haven't asked for an interview or anyhing. One of them even asked me to apply for his theorist collaborators too (I'm working experimental and it's on my CV) to make sure I have a better chance for admission. I replied them both that it would be great to work under their investigation and projects they offer are the best topics I could wish for. (That's not a lie actually, both them are quite on point by my side.)
Now I really feel that something is missing. Should I take any action afterwards? I'm open for all kinds of advice.