PTT = push to talk (at least that seems the most probable match on Wikipedia)

Doesn’t exist in Zulip, theres a “camera” button that generates a jitsi link, I tried (and failed) to make it a google meet link, but it works surprisingly well, though it is a context switch.

Yeah Google Meet doesn't have an API to just create a call; several people have tried to hook together the Calendar APIs to make a reasonable similar integration and failed.

I assume this API omission is intentional on Google's part but don't understand the motivation.

Google workspace integrates with google meet. It's likely they don't want a competitor to google chat that uses meet infra.