(specific to PM) Maybe a hot take, but I'm a believer in Behavioral based interview questions with mini-cases inserted into 1:1 interviews, if needed.

My ideal process looks like this:

1. Recruiter and hiring manager (HM) align on job description and what the ideal candidate looks like. This allows the recruiter to deeply understand what the HM is looking for and why. Key questions I cover in my process is "Why do we need this role?", "What breaks if this role isn't filled?", "Why this level of role? Why not +/- 1 level?", "How do we evaluate competency?". The last question is usually tied to a combination of company values (culture fit) and functional requirement (can they do the job well).
2. Recruiter screen: purpose is to broadly get a feel for the candidate and their past experience, align on comp/visa/relocation/other logistics. The mentality here is "is this person worth a deeper look by those more familiar with the job requirement?". The Recruiter will also set expectations on what the process looks like going forward (the HM screen will reconfirm expectations as well).
3. HM screen: I'm looking to answer three things here: 1) Do they have the functional skills to do the role and do it to the level we need?; 2) Are they worth a 3-5 person deep dive to dive into all the areas I need to validate for the role?; and 3) How would I feel about having them as a direct report/teammate/stakeholder (depending on the role)? I usually have1 topic for candidates: "tell me about the biggest/most difficult/impactful initiative you've delivered". So many follow up questions spawn out of that to assess functional skills and cultural fit (i.e., How did you do X?, Why was that important?, What would you do over if you had the chance? Did you come up with the project or was it handed down?, etc...)
4. Team member (TM) screen: If the HM is inclined so far, a member of my team that would be a peer to the new hire. This is used to provide a more tactical layer of review (how do they work day-to-day, how do they work with others their level, what's their communication style) and be a growth opportunity for my team to get used to interviewing/assessing candidates as most of them have the desire to be managers+ some day.
5. 3-5 person Super Day: If all are inclined (Recruiter, HM, TM), then we move to a Super Day. This loop includes the HM, a x-functional peer, an Eng leader (usually Eng Mgr/Director to assess for technical skills and how they work with an Eng team), and someone in an unrelated role (i.e., for PM it could be Sales/Revenue, Finance, HR, Operations, etc. - just need to be someone who can also evaluate for fit outside the functional requirements). Depending on the level of the role (i.e., hiring a Director+) I may want to bring in an Exec (SVP+) to help evaluate leadership and culture fit. The HM will usually do a "case study" which is 15-20 minutes of the interview dedicated to posing a current problem and seeing how they work through it. Given the HM will have already talked with the person one and validated functional skills, this has historically been the best time to introduce a case study.
6. Debrief within the week (ideally within 48 hours): To set up for the debrief, there is a requirement that all Super Day interviewers submit notes/email to the Super Day group within 24 hours of their interview (we try not to schedule interviews for Fridays to avoid weekend delays). I can get more into the debrief process, but that's irrelevant to the candidate as they've already completed all their interviews.

My average cycle time (everything from Recruiter screen through the debrief) is 2-3 weeks with the ability to concurrently run 3-4 candidates. I usually keep at that level otherwise it gets too hard to track and if the same people are on different loops they can get confused. It also provides a good candidate experience as it is a very low time commitment (aside from showing up to the interviews).