It has not been negligible for me, and, however you're doing this, there is significant room for improvement.

There have been times when, across about ten minutes of usage, most of which is me typing on iOS Safari, it drained 15% of my battery. There is no functional justification for this beyond poor code quality. (It was on a long conversation FWIW.)

This when I'm logged in, with a paid (Plus) account, connected to a very old email address with a real user profile. That can't be the result of super-clever bot defense measures, because it's merely an inconvenience on desktop. And if you genuinely believe that email has been compromised, why aren't you reaching out the to the account owner, as the account isn't otherwise connected to fraud by your heuristics?

However brilliant the LLM agent it is, I'm seeing a lot of unforced errors regarding how you implement a web interface to it. If it makes you feel any better, it doesn't really register compared to all the bloat I see on other sites.