But why are they doing this? What is the benefit?
If I had to guess, it’s an attempt to optimize install conversions. Every multi-step process you ask a user to perform is effectively a (marketing/sales) funnel. Some percentage of people drop off at every step. Maybe Zoom they thought that if they moved the actual installation closer to Step 1, then more people would accomplish it. It’s awfully sneaky though, especially that password dialog.
They could have also made it just work in a web browser without having to use workarounds. That's one of the reasons why I strongly prefer Google Meet and get annoyed at vendors that want me to use solutions that require me to install software.
Conversely, I much prefer a desktop app to Google Meet, since that's stuck in the browser the video can't float PIP when you navigate away from the call
It can if it uses the right web APIs, which are widely supported:
https://w3c.github.io/picture-in-picture/