Looks interesting cos I live in Chrome, often have a lot of tabs open and it could help find things. If it runs fully locally, how do the team features work?
Everything runs fully locally by default, but to enable features like sharing pages with teammates, we need to have servers. The content of your pages is still only stored locally on your browser, no exceptions. We run through the details in our privacy policy - https://www.eesel.app/privacy
Fun fact - we did consider being totally serverless and having some distributed, peer-to-peer database, but there were too many unknowns to go down that path. Maybe one day!
Only because their web client works via the phone, and their whole service is based on having a phone number; they should do a more commonplace username/password based logins (with maybe two-factor authentication on a phone) and have a regular, proper client. It's probably the biggest chat tool out there; surely they can afford to build a native client or two?
As Cthulhu_ says it's more to do with the design of their app than iOS. Now that they have the clout of Facebook behind them they should be able to come up with a solution.