Thanking Your Interviewer

If you want to express your thanks, then do it through the recruiter. (At a large enough company, I honestly don't think it'll matter much since there's a well-defined process to prevent bias.)

I remember at Meta, there was actually an incident where interviewers found it annoying to be contacted after the interview ended. I'm sure your thank you is innocuous, but looking people up on LinkedIn could send a negative signal unless they've explicitly indicated that they'd like to do that.

If you want to stand out here, I'd thank the recruiter and ask them to pass along the feedback. In your thank you note, mention specific details of the conversation that you thought were very interesting and insightful. This will increase the chance that your interviewer forwards your email or mentions it to the relevant people.

I think your intuition is correct: I would do the less heavy-handed route of going through the HR person.

The reality is that there's such a huge power dynamic in an interview, especially in this economy. Interviewers know that candidates really want the job. So their default assumption is that if the candidate is thanking them, it isn't genuine and they're just trying to score some cheap points. This is a very difficult barrier to overcome unless you have Charisma: 100.

Going through the effort to connect with them on LinkedIn and thank them there definitely feels like overreaching to me and could be taken as a negative signal.

Ideally, you show appreciative signals during the interview itself, especially if it's going well. It could be as simple as giving a genuine thanks when they give you a hint.