Is it pushy/rude to ask for more concrete feedback if the interviewer/recruiter calls says that I was a very strong candidate but they have proceeded with someone else who had more experience and explained techniques in better ways?
I found the feedback quite vague and felt like the interviewer didn't want to provide more feedback. How do I deal with a situation like this?
This is not a satisfying answer, but you just move on. Following up repeatedly or aggressively for more detailed feedback after an interview is unlikely to get you any real feedback, and it may actually backfire.
The best you can do is learn and move on: Learning from interview rejection - What kind of questions should I ask?
Sorry to hear about this and this crummy situation happens a lot in this market given the plethora of laid-off talent. It's very possible now to pass the entire interview and not get the job as some other genius candidate went through the loop and got "Strong Yes" on every round.
When it comes for feedback, it's important to set expectations very, very low as hiring companies aren't incentivized at all to give it to you for reasons I break down here: https://www.jointaro.com/course/ace-your-tech-interview-and-get-a-job-as-a-software-engineer/getting-interview-feedback/
You can try asking but make sure to be as polite and specific as possible. Use your introspection on what rounds you didn't do perfect in and ask about those. However, I would take their feedback with a grain of salt as they might make up feedback to get you off their back. Incorrect feedback is worse than 0 feedback IMHO.