Interviewed twice for this role, both times Google HR approached me.
First time was positive experience. Went through whole process (phone screens, all day onsite). Generally a time consuming process to prepare (budget on spending 1-2 weeks) but interesting. Feedback was generally pretty good, and went to hiring committee. In end didn't get role but I felt the feedback and process was fair and well run.
Google then came back 9 months later and asked if would like to try again. Was doubtful as I explained I didn't see I was going to make a 'better' performance doing again. In end was persuaded to give it a go. One upside was I skipped straight to the all day interview.
Unfortunately this is where things fall apart. Due to COVID all the interviews were moved online, which is pretty non ideal for this type of process. The setup lacked a decent whiteboarding solution which seemed amazing for a company like Google.
Interviewers this time round were ok, but definite undercurrent of arrogance and disinterest. One started my call by noting how I'd 'interviewed with us many times before' - neither accurate nor helpful. However overall I felt they went as well as the previous time, if not any better, given circumstances.
Was surprise therefore when feedback was lot more negative. What was more amazing was the HR person mentioned I could reapply again in 12 months, ignoring fact I'd already told him they approached me, and fact I'd done two rounds in 9 months. When I questioned whether they would really interview a 3rd time, assuming I was stupid enough to waste my time on it, he admitted they wouldn't - so he was just reading a script.
Overall 1st experience was a good one, 2nd time very negative.
It's clear that while Google talks a lot about diversity, there is a certain personality profile that they hire, and the interview process is set up to filter aggressively for that (even if unconsciously). In case of product management this means being good at turning out and defending an analytical / design solution to problem in 30 mins, even though the reality is that most examples are considered over weeks or months.
If you don't fit mould, and are better at thinking things over in more considered way, it's going to be a tough and time-consuming process to get through, and quite possibly a miserable experience working there if you do.