I'd be curious to investigate this; do you have many tens of thousands of unread messages in the Lean community, or is it a new account?
I ask because we have a known issue in Zulip that the first minute or two of using the product is quite slow for folks with 100K for unread messages because it the web app's client-side data fetching system ends up fetching them all in order to make clicking around the app afterwards extremely snappy.
We've reworked that system over the last few months, and it'll be deployed to Zulip Cloud next week if all goes well. But if you don't have a lot of unread messages, I'd very much like to understand why -- I'd love for you to stop by chat.zulip.org and debug with us a bit if you can spare a bit of time.
(It could be that the Lean community Zulip involves rendering a LOT of LaTeX, for example)