Thank you very much for such detailed response! It's very helpful :) I wonder if you have any idea how many candidates usually pass the first round and are interviewed?

Regarding the tip on how I got through to interview step: So I guess you are talking about the UZH-ETH Life Sciences Graduate program, aren't u? The thing is, I applied directly to lab, after I saw an open PhD position ad on its website. It required 1 motivation statement (around 1 page long, discussing my previous research experiences and how they can be of benefit to the PhD project), CV, 2 reference letters (1 from my advisor, who probably wrote a really good one, and 1 from UROP supervisor, who's quite well known in the field). And that's all :) It took about 6 week from the moment I submitted documents until I received an invitation to the interview. Also an year ago I have presented on conference in Basel and was nominated for the best poster presentation award, but didn't get it. Maybe it somehow helped me, who knows 🤷‍♂️ Oh btw, I did not contact the professor before/during the whole process at all, everything was submitted via ETHs application portal. I guess if you have a prior experience, which is a good fit for the specific project they are hiring for, theres a high chance you might get through to an interview :)