I am an international student who will apply for the Fall 2025 graduate school intake in the US (high energy theory). I have been looking at interesting papers and schools and, somewhat surprisingly, managed to schedule a few online calls with potential advisors I was considering at somewhat strong departments (I say surprising because in the US, advisors are chosen at least a year after admissions - as far as I know).
Regardless, I met these faculty online and had (what seemed to me) very fruitful and nice discussions on their future research directions, my interests and some other relevant questions (mostly pertaining to funding situations). All of the faculty seemed to encourage me to apply, were very positive about working with me (and at least a couple explicitly said that they would recommend my admission if I get shortlisted by the central committee).
This brings me to my question - how much importance should I attach to these informal meetings and encouragements?
The programs I am talking about are probably within the top 20 - 30 or so in the US and I know that faculty everywhere are too busy to just spend time on a chat with a random unknown student they haven't ever seen in their lives. But, I know that admissions are extremely competitive and, going through some of the profiles on sites like gradcafe that got rejected, I can't see how I have any shot at these places.
(The reason I ask this is because my budget is limited - so, I want to strategize accordingly and apply to places where I do have a good chance)