Has the definition of web wallet changed? As far as I can remember, people usually differentiate between web wallet and hot wallet. Stuff like MEW that is accessible through browser and apps is kinda different though, since they're effectively an app and a web wallet. I think web wallet is one where access is only available through a browser, even though some of them provide offline options or code to launch on the user''s own environment.
Web wallets have become so unpopular over the years, and people are now probably confused about them, but in our times, a web wallet was accessible through a browser. Some wallets were custodial and required one to log in using the email and password, such as the old blockchain wallet, old Coinbase web wallet, Freewallet, etc., while others were non-custodial, such as MyEtherWallet.
Most of those wallets have since evolved and do have apps and DApps.