I'm pretty sure, from previous interactions with GPT-4o and from their demos, that if you used their desktop app (which enables screensharing) and asked it to tell you where to click, step-by-step, in the Gmail web page, it would be able to do a pretty good job of navigating through it.
Let's remember that the Gmail UI is one of the most heavily documented (in blogs, FAQs, support pages, etc) in the world. I can't see GPT-4o having any difficulty locating elements in there.