How is a gpt browser useful for that?

If you're using the email addresses to provide some specific thing the user asked for, that's not lead gen, that's just "notifications" or "a newsletter" or whatever actual thing you're doing.

If someone voluntarily gives you their email address and then you send them marketing messages, the part where you collect their email address is called "lead gen". But all the other parts of that process have different names (creating a cool-looking blog is "content marketing", getting people to visit it is "SEO", sending the marketing emails is "nurturing"), and AI can't really automate the process of someone else typing their email address into a form, so in an AI context "lead generation automation" usually means either data gathering or cold outreach.