Recruiter will confirm work eligibility first, followed by a few rounds of technical interviews, including with the hiring manager and higher up management. Don't expect recruiters to be responsive. You have a higher change of getting replies by contacting the interviewers directly.

I reached out to a recruiter. She helped set up an initial phone screen which went well. Then we had another phone screen which did not go so well. The next step would've been an on site interview.