I was contacted by someone from HR almost 4 weeks after submitting my application (I had also contacted someone at Twilio directly whom I had met at a conference, but that person didn't bother to follow up).
The HR screening interview went really well and the recruiter was really nice and helpful.
The phone interview with the hiring manager went relatively well, although he chose to do it while driving so the conversation didn't go as smoothly as I hoped and I had to ask him to repeat his questions multiple times.
I managed to get to the next step, which was an at-home assignment. I spent quite a few hours researching the market and redacting my answer. I tersely heard back from the recruiter 3 days after submitting it that they would not proceed me since they felt they are candidates who were a better fit.
I wrote back to her as well as the hiring manager and asked for more feedback about what I did wrong with the assignment but I never heard back from them. I would understand the lack of feedback after a mere interview that didn't go well (even if a lot of time might have been spent preparing for that interview) but the least I would hope for when actually working many hours on an home assignment is to get some kind of detailed feedback about what was actually expected or what didn't work.
My conclusion about Twilio is that although they are in the communications business, their understanding of communication is that it's a one-way street: you can talk to them, but they don't really feel they have to reply back. They look like a great company, but they don't seem to live up to their Nine Values, especially the "Create Experiences" value ("Inspire confidence and admiration in every interaction someone has with Twilio.")